Question

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

a) -1
b) 1
c) -4
d) 4
e) 2 + 51
f) 2 - 5
g) -2 + 101
h) -2 - 101

Answer 1

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

Step-by-step explanation:

The roots of the given function g(x) = (x^2 + 3x - 4)(x^2 - 4x + 29) can be found by factoring each quadratic equation and setting them equal to zero.

The first quadratic equation x^2 + 3x - 4 = 0 can be factored as (x - 1)(x + 4) = 0, giving us two roots: x = 1 and x = -4.

The second quadratic equation x^2 - 4x + 29 = 0 cannot be factored further, so we can use the quadratic formula to find its roots. Plugging in the values a = 1, b = -4, and c = 29, we get x = -2 ± √(-2)^2 - 4(1)(29) / 2(1), which simplifies to x = -2 ± √(-100) / 2. Since the discriminant √(-100) is an imaginary number, the two roots are complex and cannot be expressed as real numbers.