Question

Solve for x: x⁴ + 9x² + 20 = 0

Answer 1

The equation is x⁴ + 9x² + 20 = 0.

By factor by grouping.

x⁴ + 5x² + 4x² + 20 = 0

x²(x² + 5) + 4(x² + 5) = 0

Factor : (x² + 5)(x² + 4) = 0

Apply zero product property.

x² + 5 = 0           and         x² + 4 = 0

x² = - 5                             x² = - 4

x = ± √ - 5                         x = ± √ - 4

→ x = ± (i√5)      and          x = ± (2i ).

The solutions are x = ± (i√5) and x = ± (2i ).