Which describes the number and type of roots of the equation x^4 - 64 = 0

a. 2 real roots, 2 imaginary roots
b. 4 real roots
c. 3 real roots, 1 imaginary root
d. 4 imaginary roots

ANSWER

a. 2 real roots, 2 imaginary roots

EXPLANATION

The given equation is

We rewrite as difference of two squares,

We factor using difference of two squares to get;

We now use the zero product property to get:

Take the square root of both sides to get;

are two real roots.

are two imaginary roots.

The correct answer is A.