If (a, 0) is a point on diameter of circle x 2 + y 2 = 4 th…

Maths Quadratic Equations Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If (a, 0) is a point on diameter of circle x 2 + y 2 = 4 then x 2 –4x – a 2 = 0 has –

Exactly one real root in (–1, 0]

Exactly one real root in [2, 5]

Distinct roots greater than –1

Distinct root less than 5

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a, b, c, d)

Max. value of a can be if it lie on circle

∴ a 2 = 4

Let f(x) = x 2 – 4x – a 2

f(0) = –a 2 < 0

f(–1) = 5 – a 2 > 0

f(2) = – 4 – a 2 < 0

f(5) = 5 – a 2 > 0

Graph can be

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