Question

Given that 7 is a zero of h(x) = x^3 - 7x^2 - 3x + 21, find the other zeros.

A) 1 and 3
B) 2 and 4
C) -3 and -1
D) 7 and -21

Answer 1

The other zeros of the polynomial h(x) = x^3 - 7x^2 - 3x + 21 are approximately -1.732 and 1.732.

Step-by-step explanation:

Given that 7 is a zero of the polynomial h(x) = x^3 - 7x^2 - 3x + 21, we can use polynomial division or synthetic division to find the other zeros.

Using synthetic division, we divide (x^3 - 7x^2 - 3x + 21) by (x-7) which yields a quotient of (x^2 + 0x - 3). This means that (x^2 + 0x - 3) is the remaining quadratic factor.

Setting (x^2 + 0x - 3) equal to zero and solving for x, we find the other two zeros to be approximately -1.732 and 1.732.