What are the real or imaginary solutions of the polynomial equation? x4 – 52x2 + 576 = 0 (1 point) Responses 4, –4 4, –4 4, –6 4, –6 4, –4, 6, –6 4, –4, 6, –6 no solution

Answer 1

The real solutions of the equation can be found by factoring the equation:

x^4 - 52x^2 + 576 = 0.

We can rewrite the equation as:

(x^2 - 16)(x^2 - 36) = 0.

Setting each factor equal to zero:

x^2 - 16 = 0,
(x - 4)(x + 4) = 0,
x = 4, -4.

x^2 - 36 = 0,
(x - 6)(x + 6) = 0,
x = 6, -6.

So the real solutions of the equation are x = 4, -4, 6, -6.

Therefore, the correct response is:

4, -4, 6, -6.