It is given the quadratic equation (q + 1 )x² - 8x + p = 0,where p and q are constants,has two equal real roots.Express p in terms of q.
Do help meeee!!!
​

Step-by-step explanation:

answer is in the photo above

Answer:

[tex]\displaystyle p = \frac{16}{q + 1}[/tex].

Step-by-step explanation:

Factor out the coefficient of [tex]x^{2}[/tex]:

[tex]\displaystyle \frac{1}{q + 1}\, [(q + 1)\, x^2 - 8\, x + p] = 0[/tex].

[tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex].

Let [tex]m[/tex] denote the real root of this equation. By the Factor Theorem, this equation would have the factor [tex](x - m)[/tex] repeated for two times in total:

[tex](x - m)^{2} = 0[/tex].

Expand to obtain: [tex]x^2 - 2\, m\cdot x + m^{2} =0[/tex].

Compare this expression with [tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex]:

[tex]\displaystyle -\frac{8}{q + 1} = -2\, m[/tex] (for the coefficient of [tex]x[/tex].)

[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex] (for the constant.)

Rewrite the first equation to find an expression for [tex]m[/tex] in terms of [tex]q[/tex]:

[tex]\displaystyle m = \frac{4}{q + 1}[/tex].

Substitute this expression for [tex]m[/tex] into the second equation to find an expression for [tex]p[/tex] in terms of [tex]q[/tex]:

[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex].

[tex]\displaystyle \frac{p}{q + 1} = \frac{4^2}{(q+1)^{2}}[/tex].

[tex]\displaystyle p = \frac{16}{q + 1}[/tex].

Verify that this expression for [tex]p[/tex] satisfies the requirements:

[tex]\displaystyle (q + 1) \, x^{2} - 8\, x + \frac{16}{q + 1} = 0[/tex].

[tex]\displaystyle x^2 - \frac{8}{q + 1} + \frac{16}{(q+1)^2} = 0[/tex].

[tex]\displaystyle x = \frac{4}{q + 1}[/tex] is the (repeated) real root of this quadratic equation.

PLEASE PLEASE ANSWER I NEED TO PASS!!!!

α
34°
Help me ASAP Thxx

ab + 4 + a + 4b


pls help if u can.

in the diagram BC = 9. find AB and AC. ​

(3х – 4у > 8
y < -2x – 7

The sum of two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?
(1 Point)

a) 84

b) 21

c) 42

d) 32
7Rakesh's mother's age is three times the present age of Rakesh. After 5 years their ages when added together, will become 66 years. The equation that represents the above is as follows;
(1 Point)

a) x + 3x = 66

b) x + 3x + 5 = 66

c) 4x + 15 = 66

d) 4x + 10 = 66
8Equation 1 is : 2 x - 3 = - 9 and Equation 2 is : x - 7 = 2. The first equation has solution (x = - 3), and the second equation has solution (x = 9) and both these answers are correct for the respective equations. Choose the correct statement from below.
(1 Point)

a) Since the first equation has a negative solution, the second equation only is a Linear equation, as it has a positive solution

b) Both equations have solutions which are rational numbers

c) The first equation is called a Negative Linear Equation as it has a negative solution

d) None of the statements a, b or c are True
9Please see the Figure A, and choose the correct
statement that matches the figure from the
options given below.
(1 Point)

a) The above figure is a Polygon with 5 sides

b) The above figure is a Concave Polygon

c) The above figure is not a Polygon

d) The above figure is a Regular Pentagon
10The sum of measures of the exterior angles of any polygon is …
(1 Point)

a) 180 degrees

b) 360 degrees

c) ( n – 2 ) x 180 degrees

d) ( n – 2 ) x 360 degrees
11In a quadrilateral, if all sides are equal and the diagonals bisect each other at right angles, then the quadrilateral …
(1 Point)

a) Is a Square

b) Is a Rhombus

c) Could be a Square, or could be a Rhombus, we need to know more about the length of the diagonals

d) None of the above statements is correct
12A rectangular wire frame could be bent and turned into a Parallelogram keeping the same 4 original sides, but the following must be true for this to happen…..
(1 Point)

a) That the diagonals remain equal

b) That the diagonals continue to bisect the angles at the vertices equally

c) The lengths of the diagonals change

d) The diagonals are now bisecting each other in 4 equal parts
13Which statement is True for the following two Figures A and B, given below
(1 Point)


a) Figure A is a Rhombus and Figure B is a Kite

b) Figure A and B are both Rhombus

c) Figure A and B are both Kites

d) Figure A is a Kite and Figure B is a Rhombus
14Which statement out of the four options below, is True?
(1 Point)

a) All Rectangles are Squares

b) All Rhombuses are Parallelograms

c) All Squares are Concave Polygons

d) All Convex Polygons have diagonals outside them
15
(1 Point)




16If 4368 ÷ 28 = 156, then if the same 4368 is now divided by 0.28, what will be the answer?
(1 Point)

a) 156

b) 15600

c) 15.6

d) 1.56
1712.00001 ÷ 0.600001 is closest to ……..
(1 Point)

a) 0.02

b) 2

c) 20

d) 200
18Complete:
(1 Point)




19The equation : 12 x + 16 = 20 is the same as ……
(1 Point)

a) 12 x + 8 = 12

b) 12 x = 20 + 16

c) 12 x – 16 = 20 – 16

d) 12 x – 20 = 16
2020. Find the value of a quarter of the angle QRT
which is ‘x’ if angle PRS is 2x as shown in the
figure below. Consider Triangle PRQ and Triangle
RST to be equilateral triangles of different sizes.
(1 Point)




21Which number will give us a quotient of - 4, if we divide - 24 by ……..
(1 Point)

a) 4

b) - 6

c) - 4

d) 6
22If 2 ( 3 – 2 x ) = 3 ( x – 5 ) then x = ……….
(1 Point)

a) – 3

b) 3

c) – 6

d) 6
23The teacher asked the class to divide a given number by 24
- Rohit divided the number by 24 and got the correct answer 20
- Mohit divided the number by 6 and got an answer which he again divided by 4 and
obtained the final answer
- Rakesh divided the number by 2.4 and then divided the answer again by 10
- Allen divided the number by 2.4 and then multiplied the answer obtained by 10

Now choose the best solution from the below options.
(1 Point)

a) Only Rohit got the correct answer

b) Both Rohit and Mohit got the correct answer

c) Rohit, Mohit and Rakesh all got the correct answer

d) Rohit, Mohit and Allen all got the correct answer
24Abhay and Binu both started walking starting at the same time and at the same rate of 5 km / hour. Abhay walked on the boundary of a big circle and Binu walked on the boundary of a small circle and both these circles were having the same center. Abhay completed 3 circles, whereas Binu completed 7 circles after half an hour. After half an hour …...................
(1 Point)

a) Abhay has walked more than Binu, as he walked on the boundary of the bigger circle

b) Binu has walked more than Abhay, as he has walked more circles than Abhay

c) Both of them have covered the same distance

d) With the information given above, we cannot say who walked more
25Which sign will you put in between [ 120 ….. ( 3 / 11 ) ], so that the answer or result is the highest number
(1 Point)

a) +

b) –

c) x

d) ÷

The measures of two exterior angles of a decagon are 97° and 89°. What is the sum of the remaining exterior angles?

Solve for X

PLEASEEEEE HELPPPP

Determine the value of x in this polygon.
(6x + 3)
(x + 12.5)°
(2x + 8)

Amanda bought 40 books. Amanda bought 8 times as many books as Hong. Let b be the number of books that Hong bought.
(a) Write an equation that relates the number of books that they bought.
Use 8, b, and 40.
40 = b x 8
(b) Find b.

wanda spent 4 1/8 hours studying last night. She spent 1/3 of the time studying math. How much time did she spend studying math?
ANSWER PLSS

Let p: x < -3 let q: x > 3 What is represented by p v q

The dimensions of Mr. Tai’s living room are 10 feet by 18 feet by 8 feet and the dimensions of his family room are 14 feet x by 20 feet by 8 feet. What is the total volume, in cubic feet, of the two rooms?

What is 4(x+1)+2(x-1) simplified?

Which set of numbers does not contain the value below?


Select one:

a. Complex Numbers
b. Pure Imaginary Numbers.
c. Rational Numbers.
d. Integers.​

Which expression is equivalent to 4x2 - 4x – 3 in factored form?

in the given figure pt is the bisector of angle qpr. qs=3x, rs=2x+2, pq=3y-1 and pr=y+5
1)solve the measure of rs
2)solve the measure of rq
3)solve the measure of pq
4)solve the measure of pr
5)solve the measure of pqsr

Which of the following is least likely to be an advantage of scientific models?


They can precisely replicate any scientific theory or law.


They can be used to help scientists formulate and improve hypotheses.


They can be used to visually represent objects that are very small or very large.


They can be used to simplify complex concepts so that they are better understood.

Help plz..And No links!! I repeat No links!!

is this a reasonable estimate? Why?

The manufacturer price was $50. The customer purchased the item for $200. What percent of the original price did the customer pay?

help me please been trying to find an answer to these questions?

The estimated total,costs,y, of a child's toy is practally based on the number of batteries used x.The cost of one battery is 0.75. The toy itself cost 12$.Which equation represents the situation

Hannah’s favourite cereal comes in 4 sizes. Which is the better buy? (Hint: check each one) *

A, 200 g for $1.58
B, 400 g for $2.97
C, 775 g for $5.49
D, 1000 g for $7.52

What percent of 8 is 1,280? A 16096 O B. 16,000% O O O C. 1,600% D. 1.6%
​

In which choice do all three points lie on the same straight line?
A (0, 1), (–1, 3), (1, 3)
B (4, 2), (2, 1), (4, –2)
C (0, 0), (8, 0), (0, 8)
D (1, 2), (2, 4), (4, 8)

A company sold 3,000 computers in one month, but 12 were returned. If 3,500 were sold the next month, the company would expect 14 to be returned.

What is a valid proportion to represent the problem?​

5 2/3 divided by 3 1/9?

Brian pays £465.98 a year on his car insurance.
The insurance company reduces the price by 3.6%.
How much does the insurance cost now?
Give your answer rounded to 2 DP.

GameStop was selling Ps5’s. They sold 100. They sold each ps5 for 500. But they got ps5’s on discount $30 off from each GameStop. So they bought the Ps5s for $470 but they sold them to the customers for more. How much did they collect/make? How much were their expenses? How much was their profit?