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Solve the following quadratic equation: x2 – 4x + 13 = 0 - Mathematics and Statistics

Sum

Solve the following quadratic equation:

x2 – 4x + 13 = 0

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Solution

Given equation is x2 – 4x + 13 = 0
Comparing with ax2 + bx + c = 0, we get
a =1, b = 4, c = 13
Discriminant = b2 – 4ac

= (– 4)2 – 4 x 1 x 13

= 16 – 52 = – 36 < 0
So, the given equation has complex roots.
These roots are given by

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

= `(-(- 4) ± sqrt(- 36))/(2  1)`

= `(4 ± 6"i")/2`

= 2 ± 3i
∴ the roots of the given equation are 2 + 3i and 2 – 3i.

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 2. (iv) | Page 40
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