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`