If where for , then has:

Maths Quadratic Equations Skill Builder Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

only one distinct real root

exactly two distinct real roots

exactly 3 distinct real roots

3 equal real roots

Text Solution

Verified by Experts

The correct answer is:

We have:

Let's analyze:

Cubic part: has 3 real roots .

Linear shift: The term shifts the cubic vertically.

Observation:

is still a cubic → at least one real root.

The derivative has 2 critical points cubic can cross -axis 3 times.

By intermediate value theorem, with increasing changes sign across each distinct real roots.

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