NDA 2020 Maths · Mathematics · Quadratic Equations · medium

If the roots of the equation x^2-6x+k=0 differ by 2, then k equals

Single correct option

If the roots of the equation

x^2-6x+k=0

differ by

2

, then

k

equals

Show answer and solution

Answer: (C) 8

Let the roots be

\alpha,\beta

with

\alpha+\beta=6

and

\alpha-\beta=2

, so

\alpha=4,\beta=2

and

k=\alpha\beta=8

. Equivalently

(\alpha-\beta)^2=36-4k=4

gives

k=8

. Value

9

would make the roots equal, and

5

gives roots

1,5

differing by

4

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake