Question

Solve the following quadratic equation:

`2x^2 - sqrt(3)  x + 1` = 0

Answer 1

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`.