Find the zeroes of the polynomial and verify the relationship between the zeroes and coefficients

1. 6x^2 - 3 - 7x
2. 3x^2 - x - 4

Answers

Answer 1

Answer: Step-by-step explanation:

1. Given  f(x) = 6x2 – 7x – 3

To find the zeros

Let us put f(x) = 0

⇒ 6x2 – 7x – 3 = 0

⇒ 6x2 – 9x + 2x – 3 = 0

⇒ 3x(2x – 3) + 1(2x – 3) = 0

⇒ (2x – 3)(3x + 1) = 0

⇒ 2x – 3 = 0 Or 3x + 1 = 0

x = 3/2                      x = -1/3

It gives us 2 zeros, for x = 3/2 and x = -1/3  

Hence, the zeros of the quadratic equation are 3/2 and -1/3.

Now, for verification

Sum of zeros = – coefficient of x / coefficient of x2

3/2 + (-1/3) = – (-7) / 6 7/6 = 7/6  

Product of roots = constant / coefficient of x2

3/2 x (-1/3) = (-3) / 6 -1/2 = -1/2

Therefore, the relationship between zeros and their coefficients is verified.

2.Let f(x) = 3x2 ˗ x ˗ 4 = 0

3x2 ˗ 4x + 3x ˗ 4  = 0

⇒ x(3x ˗ 4) + 1 (3x ˗ 4)  = 0

⇒  (3x ˗ 4) (x + 1) = 0

To find the zeroes

(3x ˗ 4) = 0 or (x + 1) = 0

x = 4/3 or x=-1

So, the zeroes of f(x) are 4/3 and x=-1

Again, Sum of zeroes = 4/3 + (-1) = 1/3 = -b/a =

=(-Coefficient of x)/(Cofficient of x2)

Product of zeroes = 4/3  x (-1) = -4/3 = c/a=

= Constant term / Coefficient of x2

Therefore, the relationship between zeros


Related Questions

A number added by 7 is the same as that
number times four minus eleven.
Translate into an equation

Answers

Answer:

[tex]x+7=4x-11[/tex]

Step-by-step explanation:

Hi there!

Let [tex]x[/tex] represent "the number".

A number added by 7 is the same as that number times four minus eleven.

A number added by 7 ⇒ [tex]x+7[/tex]

Is the same as ⇒ [tex]x+7=[/tex]

The number times four ⇒ [tex]x+7=4x[/tex]

Minus eleven ⇒ [tex]x+7=4x-11[/tex]

I hope this helps!

Someone plz round 6.675 to the nearest hundredth

Answers

Answer:

6.68

Step-by-step explanation:

To round 6.675 to the nearest hundredth consider the thousandths’ value of 6.675, which is 5. Therefore, the hundredths value of 6.675 increases by 1 to 8.

6.675 rounded to the nearest hundredth = 6.68

. If a = 120°, find the measure of angles b, c and d.
Explain your reasoning.

Answers

∡b is a vertical angle to ∡a and therefore a twin, and we know that ∡a = 120°, thus since ∡b = ∡a, ∡b = 120° as well.

a full circle has a total of 360°, ∡d and ∡c are vertical angles, namely two angles across from each other at a junction, and therefore ∡d = ∡c.

∡a + ∡b is 120° + 120° thus 240°, since a circle has a total of 360°, 360 - 240 = 120, so the other two angles pick up that slack and divide it among each other evenly, 120/2 = 60, so ∡d = ∡c = 60°.

A shopkeeper fixed the marked price of his radio to make a profit of 30 %. Allowing 15 % discount on the marked price, the radio was sold. What percent profit did he make? ​

Answers

Answer:

10.5 %

Step-by-step explanation:

Here .

let the Cost Price be 'x'

the..

by the question..

the marked price was fixed to make 30% profit

then..

the marked price will be

x+ 30% of x

= x + 30/100 × x

=x+ 0.3x

=1.3x

soo .. the marked price is 1.3x

now.. after allowing 15% discount..

the selling price will be

1.3x - 15% of 1.3x

= 1.3x - 0.195x

= 1.105x

thank you...

plzz mark me brainliest now

now..

profit made = 1.105x-x

= 0.105x

soo .

in percentage..

profit percent = profit/cp × 100%

= 0.105x/x × 100%

= 10.5 %

If A=(prime number less than 10)list the element of set A and find n(A)​

Answers

A=(2 3 5 7)
N(A) =4


( sorry I need the points)

Find the distance between the two points.
(5,5)
(2.2)
✓ [?]
Enter the number that
goes beneath the
radical symbol.

Answers

Answer:

[tex]{18}[/tex]

Step-by-step explanation:

[tex] \sqrt{(2 - 5) {}^{2} + ( 2 - 5) {}^{2} } [/tex]

[tex] = \sqrt{( - 3) {}^{2} + ( - 3) {}^{2} } [/tex]

[tex] = \sqrt{9 + 9} [/tex]

[tex] = \sqrt{18}[/tex]

Answered by GAUTHMATH

i need help now! Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work.

Answers

Answer:

i cant see a parrellogram!

please post a picture

Fill in the table to explore the graph.
Miles Walked by Alonso
" Time (hours) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Miles Walked
6
V
16
12
Miles
8
4
X
1
4
3
Time (hours)
time

Answers

Answer:

Step-by-step explanation:

so you have divide  ok by my  and divide 5x1

[tex]\sqrt[3]{x+1} =2x+2[/tex]

Answers

the answer is down below

On a recent math test. Samantha scored 3 points for each of the 18 multiple choice que non se
answered correctly and 5 points for each of the 6 short response questions she answered correctly
She scored an additional 4 points for the bonus question. Write an expression for her total score on
the test and then find her score.

Answers

The required expression will therefore be:

(3×18) + (5×6) + 4

Her total score is 88points :

From the question given, we are told that Samantha scored 3 points for each of 18multiple questions his means that the total points made here is expressed as:

(3 × 18) ...1

If she got 5 points for each of the 6 short responsmultiple choice questione questions she answered

correctly, the total point made will be expressed as;

(5×6) ... 2

Total score for an additional 4 points for the bonus question will be "4"

Expression for her total score will be the sum of all the expression above as thus:

(3×18) + (5×6) + 4

Taking the sum, her score will be:

= (3×18) + (5×6) + 4

= 54 + 30 + 4

= 84 + 4

= 88 points

The required expression will therefore be:

(3×18) + (5×6) + 4

Her total score is 88points

Learn more about sum here: brainly.com/question/16397188

How do I do question 2?

Answers

Answer:

518

Step-by-step explanation:

solution:

=8^2^×1^+1+6^2^×1^-1

=8^3+6^1

=8^3+6

=8×8×8+6

=512+6

=518

how to change mixed fraction into improper fraction and improper to proper fraction easy way

Answers

To convert a mixed fraction to an improper fraction, follow these steps:

Step-by-step explanation:

Multiply the whole number part by the fraction's denominator.Add that to the numerator.Then write the result on top of the denominator

Hope this helps you ❤️

MaRk mE aS braiNliest ❤️

Answer with Step-by-step explanation:

To change the mixed fraction into improper fraction you multiply the denominator with the whole and add to numerator.

For example:  4 1/5 = (5*4)+1/5=21/5

To change improper into proper mixed fraction,

Divide the numerator by denominator and write the remainder on numerator

For example: 7/2= 3 1/2

Which of the following numbers is between 0.08 and 0.4?
(A) 0.019
(B) 0.009
(C) 0.109
(D) 0.91
(E) 0.409

Answers

Answer:

C

Step-by-step explanation:

the numbers between 0.08 and 0.4 are:

0.09, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15, .16, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39

I bolded the number closest to your answer choices, hope this helps!

I need help I don't understand it.

Answers

These angles are corresponding angles, and we know that corresponding angles are equal when a transversal intersects two parallel lines.

So,

8x - 12 = 6x + 8

=> 8x - 6x = 8 + 12

=> 2x = 20

=> x = 20/2

=> x = 10

So, the value of x is 10.

8x-12=6x+88x-6x=8+122x=20x=20÷2x=10

please mark this answer as brainlist

How many tacos could you buy with your money? On Tuesday you can buy two tacos and you get one free.

If you had $20 dollars would you have enough money to buy a taco for 37 students on a Tuesday?

Answers

Answer:

due to not much information given and the way you ask the question I would definitely say no

Answer:

Yes you would have enough!

Step-by-step explanation:

Simply multiply .50 by 37 and that gives you 18.5!

Seventy-two books were to be divided up among 18 children. Which of the following
expressions is equivalent to this fraction?
a. 8/3 divided by 6/9
b. 8/3 times 2/3
c. 2/9 divided by 8/9
d. 2 times 8/2

Answers

Answer:

a

Step-by-step explanation:

cause if 72 book were divided by 18 kids they would hav all gotten 4 books each

so a is the answer cause it gives youthe answer 4

Answer: a. 8/3 divided by 6/9

Step-by-step explanation: I got this question on my test

The product of two numbers is 10000.If one number is 16 times the other numbers ,find the two numbers.​

Answers

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

➯Question:

The product of two numbers is 10000. If one number is 16 times the other numbers ,find the two numbers.

Answer:

Both numbers are 25 and 400.

Step By Step Explanation:

Given that:

The product of two numbers is 10000.

One number is 16 times the other number.

To Find:

Both numbers?

Solution:

Let us consider that one number be n, in question it is stated that other number is 16 times the first number. Therefore, other number is 16n.

According to the Question :

[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]

Hence,

1st number = n = 25

2nd number = 16n = 16 × 25 = 400

∴ Hence, both numbers are 25 and 400.

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

(25, 400) or (-25, - 400)

Step-by-step explanation:

Let the numbers be x and y.

We have:

y = 16xxy = 10000

Substitute y and solve for x:

x(16x) = 1000016x² = 10000x² = 10000/16x² = 625x = √625x = ± 25

Then y is:

y = ± 25*16 = ± 400

The numbers are:

25 and 400 or -25 and - 400

Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height

pls help​

Answers

Answer:

8% out of 175 = ( 8 ÷ 100 ) × 175 = 14

175 cm - 14 = 161 cm

...............

Solve the system of equations.
y = x2 + 3x - 4
y= 2x - 4

Answers

Answer:

The two solutions are

(0,-4) and (-1,-6)

Step-by-step explanation:

The ys have to be equal so you can equate the right hand side.

x^2 + 3x - 4 = 2x - 4         Add 4 to both sides

x^2 + 3x = 2x                    Subtract 2x from both sides

x^2 + 3x - 2x = 0              Combine

x^2 + x = 0                       Factor

x(x + 1) =0

Just to show you that these two points really are the solutions, you can see the graph below

x has 2 values

x + 1 = 0

x = - 1

or

x = 0

Now solve for y

y = 2x - 4

Let x = 0

y = - 4

Let x = - 1

y = 2x - 4

y = -2 - 4

y = - 6

The blue is y = x^2 + 3x - 4

The green line is y = 2x - 4

elizas backpack weights 18 7/8 pounds with her math book in it. without her math book, her backpack weighs 14 7/9 pounds

Answers

I'm assuming your trying to find the weight of the math book so here it is:

Answer:

4 5/36

Step-by-step explanation:

You'd have to do 18 7/8 - 14 7/9 but you can't subtract them yet because they don't have common denominators. So, you have to multiply the 7/8 by 9 and the 7/9 by 8. Then you would get 63/72 and 56/72. Then you put that into the equation and get, 18 63/72 - 14 53/72. If you subtract those, you get the answer, 4 10/72. Which can be simplified as 4 5/36.

HELLLPPPPPPPPP!!!!!!

Answers

ANSWER:

9) If the season is summer, then it also does not snow.

10) If you live in Salem, then you also live in Oregon.

(I’m not sure if I formatted these correctly in sentences, but hopefully you can see the pattern!)

Please help! Geometry 9th grade

Answers

Answer:

69.3

Step-by-step explanation:

if you put it into 2D, you get a right triangle with leg lengths 62 (vertical height) and 31 (1/2 the base's length). Using Pythagorean's Theorem you get sqrt((62^2)+(31^2))= 69.318. Rounding to the nearest tenth you get 69.3

Brainliest if you help me ….

Answers

-15 is the answer your welcome

What is the equation of the following graph in vertex form?
Y=(X-3)^2-1
Y=(X+3)^2-1
Y=(X-4)^2-2
Y=(X-4)^2+8

Answers

Answer:

Hello,

answer B

Step-by-step explanation:

Vertex is (-3,-1)

The equation of the parabola should be:

y=k*(x+3)²-1

(0,8) is a point of the parabola:

8=k*(0+3)²-1

8+1=9k

k=1

Equation is y=(x+3)²-1

Answer B

What is the area of trapezoid DEFG?
PLEASE SO THIS ASAP!!!
MUST SHOW WORK

Answers

Answer:

Area = 35 cm^ 2

Step-by-step explanation:

Area = 1/2(a+b) x h

1/2 (5+9) x 5

= 35 cm^ 2

Answered by G a u t h m a t h

Answer:

A = 35  cm²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height between the bases and b₁, b₂ are the bases.

Here h = 5 , b₁ = 9 and b₂ = 5 , then

A = [tex]\frac{1}{2}[/tex] × 5 × (9 + 5) = 2.5 × 14 = 35 cm²

How many integers $n$ satisfy $-4n\ge 12$ and $n+5>2$??

Answers

-4n ≥ 12   ==>   n ≤ -3

n + 5 > 2   ==>   n > -3

But n cannot be both less than/equal to -3 AND greater than -3, so there are no integers n that satisfy these inequalities.

Answer: 0

Step-by-step explanation:

My hw says, "suppose E has a coordinate of -1 And EG= 7" what is the possible coordinate of G?​

Answers

Answer:

-8,6

Step-by-step explanation:

from what i can tell this is a 1D problem. |E-G|=7, and E=-1, so -1-G=+-7. G=-8 or 6

Answer: Wouldn’t the possible coordinate of G be 8?

Step-by-step explanation:

If E is -1 and we know that EG combined is 7, we can deduce that you have to have an 8 to get 7 because 8 + -1 = 7 or E + G = EG

Find slopes of the given points .


[tex]\Large\star\tt {(5,6)\atop (3,-2)}[/tex]
[tex]\Large\star\tt {(-3,4)\atop (4,-7)}[/tex]


Spam free answers required .

Well explained answer will be marked as brainliest .​

Answers

Answer:

Use the slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

The first one:

m = (-2 - 6)/(3 - 5) = -8/-2 = 4

The second one:

m = (-7 - 4)/(4 - (-3)) = -11/7

Answer:

Step-by-step explanation:

1)  (x₁,y₁) = (5 , 6)   &  (x₂,y₂) = (3 , -2)

[tex]Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-2-6}{3-5}\\\\=\dfrac{-8}{-2}\\\\=4[/tex]

2) (x₁,y₁) = (-3, 4)   &  (x₂,y₂) = (4 , -7)

[tex]Slope= \dfrac{-7-4}{4-[-3]}\\[/tex]

           [tex]= \dfrac{-11}{4+3}\\\\=\dfrac{-11}{7}[/tex]

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!

Answers

Answer:

D

Step-by-step explanation:

we take the base as a right angled triangle with sides 6mi , 8 mi and hypotenuse 10 mi.

area of base=1/2×6×8=24 mi²

volume=base area ×height

=24×8

=192 mi³

Answer:

D

Step-by-step explanation:

Please help!!!!!!!!!!​

Answers

Answer:

b) 7 (1, 2,3,5,7,11,13)

c) 0

d) 5

e) 8

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