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.