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Maths Quadratic Equations Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If the roots of the equation x 2 – px + q = 0 differ by unity then

p 2 = 1 – 4q

p 2 = 1 + 4q

q 2 = 1 – 4p

q 2 = 1 + 4p

Text Solution

Verified by Experts

The correct answer is:

Suppose the equation x 2 – px + q = 0 has the roots α α + 1

and α α then α α + 1+ α α = p ⇒ ⇒ 2 α α = p – 1 . . . . (1)

and ( α α +1) α α = q ⇒ ⇒ α α 2 + α α = q. . . . .. (2)

Putting the value of α α from (1) in (2), we get

⇒ ⇒ (p – 1) 2 + 2(p – 1) = 4q

⇒ ⇒ p 2 – 1 = 4q ⇒ ⇒ p 2 = 4q + 1.

Alternative: Let α α and β β be the roots. | α α – β β | = 1

⇒ ⇒ ( α α + β β ) 2 – 4 α α β β = 1

⇒ ⇒ p 2 – 4q = 1, or p 2 = 1+ 4q

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