CAT 2020 Exam Shift 1 Solved Paper

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Question : 68 of 76

Marks: +1, -0

If

f(5+x)=f(5-x)

for every real

x

, and

f(x)=0

has four distinct real roots, then the sum of these roots is

0
40
10
20

Solution:

Given

f(5+x)=f(5-x)

Put

x=x-5

f(x)=f(10-x)

∴

Let

a, b

be two roots of

f(x)=0

, then

10-a, 10-b

are also roots of

f(x)=0

∴

Hence sum of the roots

=a+b+10-a+10-b=20

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