Question

State the number of complex roots and the possible number of real and imaginary roots for each equation.

(x2 + 9) (x2 +6) = 0

Answer 1

The given equation has four real roots and zero complex roots.

Step-by-step explanation:

The given equation is (x2 + 9)(x2 + 6) = 0. To determine the number of complex roots, we need to find the number of distinct quadratic factors with no real roots. In this case, both factors have real roots since x2 + 9 = 0 has two complex roots and x2 + 6 = 0 has two real roots.

Therefore, the given equation has a total of four real roots and zero complex roots.