Question

Solve the following quadratic equation.

x² + 3ix + 10 = 0

Answer 1

Comparing the equation x² + 3ix + 10 = 0 with ax² + bx + c = 0, we have,

a = 1, b = 3i, c = 10

∴ b² – 4ac = (3i)² – 4(1)(10)

= 9i² – 40 = – 9 – 40   ...[∴ i² = – 1]

= –  49 < 0

So, the equation has complex roots. These roots are given by

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

= `(-3"i" ± sqrt(-49))/(2(1))`

= `(-3"i" ±7"i")/2`

Hence, the roots of the equation are,

`(-3"i" + 7"i")/2` and `(-3"i" - 7"i")/2`, i.e., 2i and – 5i.