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 2 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 `ax^2 + bx + c` = 0

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

∴ Discriminant, `D = b^2 - 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.