If and where, , then has at least real rootsFind .

Maths Quadratic Equations Solution of Quadratic Inequations and Miscellaneous Equations Numeric Response

Published by: CGP EDU Academic Team

Published on: August 11, 2026

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The correct answer is:

(2)
Sol. Let all four roots are imaginary. Then roots of both equations and are imaginary.

Thus , So , which is impossible unless .

So, if or at least two roots must be real.

If , we have the equations.

and

or as one of and must be positive, so two roots must be real.

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