CAT 2022 Slot 2 Paper

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Question : 47 of 66

Marks: +1, -0

The number of integer solutions of the equation $(x^2-10)(x^2-3x-10)=1$ is

Your Answer:

Solution:

Case 1: When

x^2-3 x-10=0

and

x^2-10 ≠ 0

x^2-3 x-10=0

or,

(x-5)(x+2)=0

or,

{\x}=5

or -2
Case 2:

x^2-10=1

x^2-11=0

No integer solutions
Case 3:

x^2-10=-1

and

x^2-3 x-10

is even

x^2-9=0

or,

(x+3)(x-3)=0

or,

{\x}=-3

and 3
for

{\x}=-3

and

+3 x^2-3 x-10

is even
In total 4 values of

x

satisfy the equations

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