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Question

If x is real and k=x2x+1x2+x+1 the:

A
k[13,3]
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B
k3
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C
k13
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D
None of these
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Solution

The correct option is D k[13,3]
We have,
k=x2x+1x2+x+1
or, k(x2+x+1)=(x2x+1)
or, x2(k1)+x(k+1)+(k1)=0
For the above equation x will be real if the discreminant 0.
(k+1)24(k1)20
or, 10k3k230
or, 3k210k+30
or, 3k29kk+30
or, 3k(k3)1(k3)0
or, (k3)(3k1)0
13x3
or, x[13,3].

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