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Mathematics
Keyla Daniel
15 July, 03:43
If f (x) = x^2 - 4 (x) + 6, find x if f (x) = 27
+5
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Gia Orozco
15 July, 05:08
0
x = - 3 or x = 7
Step-by-step explanation:
Given
f (x) = x² - 4x + 6
If f (x) = 27, then equating gives
x² - 4x + 6 = 27 (subtract 27 from both sides)
x² - 4x - 21 = 0 ← in standard form
Consider the factors of the constant term ( - 21) which sum to give the coefficient of the x - term ( - 4)
The factors are - 7 and + 3, since
- 7 * 3 = - 21 and - 7 + 3 = - 4, hence
(x - 7) (x + 3) = 0
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 7 = 0 ⇒ x = 7
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