Question

Solve the following quadratic equation.

2x² + 3ix + 2 = 0

Answer 1

Given equation is 2x² + 3ix + 2 = 0

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

a = 2, b = 3i, c = 2

Discriminant = b² – 4ac

= (3i)² – 4 × 2 × 2

= 9i² – 16

= – 9 – 16   ...[∵ i² = – 1]

= – 25 < 0

So, the given equation has complex roots.

These roots are given by

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

= `(-3"i" ± sqrt(-25))/(2(2))`

∴ x = `(-3"i" ± 5"i")/4`

∴ x = `(-3"i" + 5"i")/4` or x = `(-3"i" - 5"i")/4`

∴ x = `1/2`i or x = – 2i

∴ the roots of the given equation are `1/2`i  and – 2i.