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Solve the following quadratic equation: 2x2 + 3ix + 2 = 0 - Mathematics and Statistics

Sum

Solve the following quadratic equation:

2x2 + 3ix + 2 = 0

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Solution

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.

Concept: Solution of a Quadratic Equation in Complex Number System
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Exercise 3.2 | Q 3. (ii) | Page 40
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