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Question

Let y2=(x+5)(x−3)x−1, then all the real values of x, for which y has non-zero real values, are:

A
-5 < x < 1
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B
x > 15
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C
-5 < x < 1 or x > 3
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D
None of these
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Solution

The correct option is C -5 < x < 1 or x > 3
If y is real and non-zero y2>0,i.e.,(x+5)(x3)(x1)>0
Case (i) : If numerator and denominator are > 0
x>3 or x<5 and x>1
But with x < -5 , y2 is negative which is not possible.
Case (ii): If numerator and denominator are < 0
5<x<3 and x<1.

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