I’m so stumped on this problem: “If there is only one solution to the equation 0= -x^2 + bx - 8 what are the possible values of b?

Answer 1

-x² + bx - 8 = 0

x² - bx + 8 = 0

To have only one solution, the quadratic expression must be of the form (x - k)², and the solution is x = k.

(x - k)² = x² - bx + 8

x² - 2kx + k² = x² - bx + 8

Comparing terms,

-2k = -b ⇒ b = 2k

k² = 8 ⇒ k = √8

b = 2√8

Test the answer:

(x - 2√8 x + 8) = (x - √8)²

Note the only solution is √8.