Solve each equation State the number and type of roots x4 8

Solve each equation. State the number and type of roots.

x⁴ - 81 = 0

Solution

x⁴ - 81 = 0

(x²)²-9² =0

a²-b²=(a-b)(a+b)

(x²+9)(x²-9) =0

(x²+9)=0,(x²-9) =0

x²=-9 ,x²=9

x=-(-9), x=-9, x=9 ,x=-9

x=-3i, x=3i, x=3 ,x=-3

4 roots:

-3i,3i are complex roots , -3,3 are real roots