Need help for one function question

Question

Let f(x) be a quadratic function such that f(x)=7 has one solution. The product of the roots of f(x) is 32. What is the sum of the roots of f(x)?

It would be greatly appreciated if the steps were included

Answer 1

I understood the question differently. That a solution of f(x) = 7

For a quadratic:

Let the roots be a and b. ab= 32

f(x) = (x-a)(x-b) = x² -(a+b)x + ab = x² -(a+b)x + 32 = 0

if f(x) = 7 --> x² -(a+b)x +32 = 7 or g(x) = x² - (a+b)x + 25 = 0

Factors of 25 are 1, 25, -1, -25

f(1) = 1 - (a+b) +32 = 7 --> (a+b) = -26

turns out for 1, -1, 25 and -25, (a+b) = -26

Answer 2

Hi Chleo

If what I understand the question correctly. By solution of f(x) = 7 you mean that the a root is located at x = 7.

1.) I assume the first half of the quadratic is (x - 7)

2.) I mulitply 7 times x to equal 32

7x = 32

x = 32/7

3.) this means the other part to the quadratic is (x - 32/7)

4.) the sum of the roots are

7 + 32/7

7 *(7/7) + 32/7

49/7 +32/7

81/7

for fun the quadratic would be (x - 7) (x - 32/7) or x² - (81/7)x + 32