Question

Solve the following quadratic equation.

ix² − 4x − 4i = 0

Answer 1

ix² − 4x − 4i = 0

Multiplying throughout by i, we get

i²x² − 4ix − 4i² = 0

∴ −x² − 4ix + 4 = 0  ...[∵ i² = − 1]

∴ x² + 4ix − 4 = 0

Comparing with ax² + bx + c = 0, we get

a = 1, b = 4i, c = − 4

Discriminant = b² − 4ac

= (4i)² − 4 × 1 × − 4

= 16i² + 16

= − 16 + 16

= 0

So, the given equation has equal roots.

These roots are given by

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

= `(-4"i" ± sqrt(0))/(2(1))`

= `(-4"i")/2`

∴ x = − 2i

∴ the roots of the given equation are − 2i