Question

Two roots of a 3-degree polynomial equation are 5 and -5. Which of the following cannot be the third root of the equation ?

0
-5i
-5
5i
5

Answer 1

- 5i and 5i

Explanation:

The Fundamental theorem of Algebra states that a polynomial of degree 3 has 3 roots, real and/ or complex.

Complex roots occur in conjugate pairs.

Given 2 real roots x = 5, x = - 5

There cannot be complex roots as they occur in pairs which would result in the polynomial having 4 roots instead of 3.