Question

Solve the following quadratic equation.

x² + 4ix − 4 = 0

Answer 1

Comparing the equation x² + 4ix − 4 = 0 with ax² + bx + c = 0, we have,

a = 1, b = 4i, c = − 4

∴ b² − 4ac = (4i)² − 4(1)(− 4)

= 16i² + 16

= − 16 + 16    ...[∵ i² = − 1]

= 0

So, the roots are equal. These roots are given by

x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`

= `(-4"i" ± sqrt(0))/(2(1))`

= − 2i

Hence, the roots of the equation are equal and it is − 2i.