Question

Which of the following equations has two distinct real roots?

Options

• `2x^2 - 3sqrt(2)x + 9/4` = 0

• `x^2 + x - 5` = 0

• `x^2 + 3x + 2sqrt(2)` = 0

• `5x^2 - 3 + 1` = 0

Answer 1

`x^2 + x - 5` = 0

Explanation:

The given equation is `x^2 + x - 5` = 0

On comparing with `ax^2 + bx + c` = 0

We get a = 1, b = 1 and c = –5

The discriminant of `x^2 + x - 5` = 0 is 

`D = b^2 - 4ac = (1)^2 - 4(1)(-5)`

= 1 + 20

= 21

⇒ `b^2 - 4ac > 0`

So, `x^2 + x - 5` = 0 has two distinct real roots.