Question

Given that f(x) = x^3 + 2x^2 + 1, g(x) = −x^3 −x^2 −4x+ 4, h(x) = f(x) +g(x), and h(x) = 1, what is the value of x?

Answer 1

x = 2

Explanation:

h(x) = f(x) + g(x) = x³ + 2x² + 1 - x³ - x² - 4x + 4 ← collect like terms, thus

h(x) = f(x) + g(x) = x² - 4x + 5

Given

h(x) = 1, then

x² - 4x + 5 = 1 ( subtract 1 from both sides )

x² - 4x + 4 = 0 ← in standard form

(x - 2)² = 0 ← in factored form ( perfect square ), thus

x - 2 = 0 ⇒ x = 2