Question

Identify all of the roots of g(x)=(x^2+3x-4)(x^2-4x+29)

Answer 1

The roots of g(x)=(x^2+3x-4)(x^2-4x+29) are x = -4, x = 1, and the complex roots of x^2-4x+29 = 0.

Step-by-step explanation:

To identify all the roots of g(x)=(x^2+3x-4)(x^2-4x+29), we need to find the values of x that make g(x) equal to zero.

First, we set each factor equal to zero and solve for x:

1. x^2+3x-4 = 0
   Solving this quadratic equation gives x = -4 or x = 1.
2. x^2-4x+29 = 0
   This quadratic equation does not have any real roots. The discriminant is negative, so there are no real solutions.

Therefore, the roots of g(x) are x = -4, x = 1, and the complex roots of x^2-4x+29 = 0.