Question

The given quadratic equation `3x^2 + sqrt7x + 2 = 0` has ______.

Options

• two equal real roots.

• two distinct real roots.

• more than two real roots.

• no real roots.

Answer 1

The given quadratic equation `3x^2 + sqrt7x + 2 = 0` has no real roots.

Explanation:

The given equation is `3x^2 + sqrt7x + 2 = 0`.

Comparing is with ax² + bx + c = 0, we get

a = 3, b = `sqrt7`, and c = 2

∴ D = `b^2 − 4ac = (sqrt7)^2 − 4 × 3 × 2`

= 7 − 24 = − 17

D < 0.

So, the given equation has no real roots.