Question

Solve the following quadratic equation:

x² + 4ix – 4 = 0

Answer 1

Given equation is x² + 4ix – 4 = 0
Comparing with ax² + bx + c = 0, we get
a = 1, b = 4i, c = – 4
Discriminant = b² – 4ac
= (4i)² – 4 x 1 x – 4
= 16i² + 16
= – 16 + 16      ...[∵ i² = – 1]
= 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 and – 2i.