Question

Solve the following quadratic equation:

x² + 3ix + 10 = 0

Answer 1

Given equation is x² + 3ix + 10 = 0
Comparing with ax² + bx + c = 0, we get
a = 1, b = 3i, c = 10
Discriminant = b² – 4ac

= (3i)² – 4 x 1 x 10

= 9i² – 40

= – 9 – 40      ...[∵ i² = – 1]

= – 49 < 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(-49))/(2(1)`

∴ x = `(-3"i" + 7"i")/2`

∴ x = `(-3"i" + 7"i")/2 or x = (-3"i" - 7"i")/2`

∴ x = 2i or x = – 5i
∴ the roots of the given equation are 2i and – 5i.