Multiple choice

Read the following information and answer the three items that follow : Let $f(x) = x^2 + 2x - 5 $ and $g(x) = 5x + 30$ What are the roots of the equation $g[f(x)] = 0$ ?

  1. $1, -1$
  2. $-1, -1$
  3. $1, 1$
  4. $0, 1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

g[f(x)] = 5(x^2 + 2x - 5) + 30 = 0. 5x^2 + 10x - 25 + 30 = 0. 5x^2 + 10x + 5 = 0. x^2 + 2x + 1 = 0. (x+1)^2 = 0. x = -1, -1.

AI explanation

First substitute f(x) into g(x) to get g(f(x)) = 5(x^2 + 2x - 5) + 30. Simplifying this expression yields 5x^2 + 10x + 5. Setting this equal to zero and dividing by 5 gives x^2 + 2x + 1 = 0. Factoring the quadratic gives (x+1)^2 = 0, which has the repeated root x = -1. Therefore, the roots are -1 and -1.