# Which of the following equations has two distinct real roots? - Mathematics

MCQ

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

#### Solution

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.

Concept: Nature of Roots
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10