JEE Main 2024 · Mathematics · Quadratic Equations · medium

Let m be real. Both roots of x^2-2mx+m^2-4=0 lie strictly inside the interval (-1,7) exactly when p<m<q. The value of q-p is

Single correct option

Let

m

be real. Both roots of

x^2-2mx+m^2-4=0

lie strictly inside the interval

(-1,7)

exactly when

p<m<q

. The value of

q-p

Show answer and solution

Answer: (C) $4$

The quadratic factors as

(x-m)^2=4

, so its roots are

m-2

and

m+2

. Both lie in

(-1,7)

iff

m-2>-1

and

m+2<7

, that is

m>1

and

m<5

. Hence

p=1

q=5

and

q-p=4

. A common slip is to take the width of the given interval (

8

) or to forget that two conditions, one for each root, must hold together; the discriminant is

16>0

for every

m

, so it adds no restriction.

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