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

x² + x – 5 = 0

Explanation:

The given equation is x² + x – 5 = 0

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

a = 1, b = 1 and c = – 5

The discriminant of x² + x – 5 = 0 is 

D = b² – 4ac

= (1)² – 4(1)(–5)

= 1 + 20

= 21

⇒ b² – 4ac > 0

So, x² + x – 5 = 0 has two distinct real roots.