172k views
0 votes
Two roots of a 3-degree polynomial equation are 5 and -5. Which of the following cannot be the third root of the equation?

There are multiple answers.
5
5i
0
-5
-5i

User Eli Burke
by
7.0k points

2 Answers

5 votes
Imaginary roots always occur in pairs never on their own.
Therefore 5i and -5i cannot be the third root.
User Eicksl
by
6.9k points
6 votes

Answer:

Option 2 and 5.

Explanation:

It is given that two roots of a 3-degree polynomial equation are 5 and -5.

The number of roots is equal to the degree of the polynomial.

Degree of the polynomial is 3 it means the number of roots is 3.

According to the complex conjugate root theorem if a complex number a+ib is a root of polynomial P(x) then its conjugate a-ib is also the root of P(x). It means the number of complex root is always even.

Two given roots are real, so the remaining single root must be a real number.

So, 5i and -5i can not be the third root of the equation.

Therefore, the correct options are 2 and 5.