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Solve the following quadratic equation: x2 + 4ix – 4 = 0 - Mathematics and Statistics

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Sum

Solve the following quadratic equation:

x2 + 4ix – 4 = 0

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Solution

Given equation is x2 + 4ix – 4 = 0
Comparing with ax2 + bx + c = 0, we get
a = 1, b = 4i, c = – 4
Discriminant = b2 – 4ac
= (4i)2 – 4 x 1 x – 4
= 16i2 + 16
= – 16 + 16      ...[∵ i2 = – 1]
= 0
So, the given equation has equal roots.
These roots are given by

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

= `(-4"i" +- sqrt(0))/(2(1)`

= `(-4"i")/2`

∴ x = – 2i
∴ the roots of the given equation are – 2i 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. (iii) | Page 40
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