Question

The function f is such that f(x) = x^2 – 2x + 3

Solve f(x) = 27

(The bottom question in the photo)

Answer 1

f(x)= 27

x^2 -2x+3=27

×^-2x+3-27=0

x^2x-24=0

(x-6)(x-4)=0

x-6=0 or ×-4=0

×=6or ×=4

Answer 2

x = - 4, x = 6

Explanation:

Given

f(x) = x² - 2x + 3 and f(x) = 27, then equating the 2 gives

x² - 2x + 3 = 27 ( subtract 27 from both sides )

x² - 2x - 24 = 0 ← in standard form

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)

The factors are - 6 and + 4, since

- 6 × 4 = - 24 and - 6 + 4 = - 2, thus

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4