Question

Determine the number of x-intercepts that appear on a graph of each function. f (x) = (x + 2)(x - 1)[x - (4 + 3i )][x - (4 - 3i)]

Answer 1

This function has two x-intercepts.

Explanation:

The number of x-intercepts of a function is given by the number of REAL ROOTS of the function. A complex root does not intercept x.

In this function, we have

Two real roots: x = -2 and a x = 1

Two complex roots: x = -4 + 3i and x = -4 - 3i

So this function has two x-intercepts.

Answer 2

f(x) has two real roots, -2 and +1. Those are the only x-intercepts.

f(x) has 2 x-intercepts.