Mathematics

Question

The function f is such that f(x) = x^2 – 2x + 3
Solve f(x) = 27

(The bottom question in the photo)
The function f is such that f(x) = x^2 – 2x + 3 Solve f(x) = 27 (The bottom question in the photo)

2 Answer

  • Answer:

    x = - 4, x = 6

    Step-by-step 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

  • 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