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Sum

**Solve the following quadratic equation: **

x^{2} + 3ix + 10 = 0

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#### Solution

Given equation is x^{2} + 3ix + 10 = 0

Comparing with ax^{2} + bx + c = 0, we get

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

Discriminant = b^{2} – 4ac

= (3i)^{2} – 4 x 1 x 10

= 9i^{2} – 40

= – 9 – 40 ...[∵ i^{2} = – 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.

Concept: Solution of a Quadratic Equation in Complex Number System

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