Question

The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.

Options

• two distinct real roots

• two equal real roots

• no real roots

• more than two real roots

Answer 1

The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has no real roots.

Explanation:

Given equation is `2x^2 - sqrt(5)x + 1` = 0

On comapring with ax² + bx + c = 0, we get

a = 2, b = `-sqrt(5)` and c = 1

∴ Discriminant, D = b² – 4ac

= `(-sqrt(5))^2 - 4 xx (2) xx (1)`

= 5 – 8

= – 3 < 0

Since, discrimant is negative,

Therefore quadratic equation `2x^2 - sqrt(5)x + 1` = 0 has no real roots

i.e., imaginary roots.