# Solve the following quadratic equation: 2x2-3 x+1 = 0 - Mathematics and Statistics

Sum

2x^2 - sqrt(3)  x + 1 = 0

#### Solution

Given equation is 2x^2 - sqrt(3)  x + 1 = 0
Comparing with ax2 + bx + c = 0, we get
a = 2, b = -sqrt(3), c = 1
Discriminant = b2 – 4ac

= (-sqrt(3))^2 - 4 xx 2 xx 1

= 3 – 8 = – 5 < 0
So, the given equation has complex roots.
These roots are given by

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

= (- - sqrt(3) +- sqrt(-5))/(2(2))

∴ x = (sqrt(3) ± sqrt(5)"i")/4

∴ the roots of the given equation are

(sqrt(3) + sqrt(5)"i")/4 and (sqrt(3) - sqrt(5)"i")/4.

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. (ii) | Page 40