NIMCET 2016 Question Paper with solutions

Question : 90 of 120

Marks: +1, -0

The number of points in (- ∞ , ∞) , for which

x^2

– x sin x – cos x =0 is;

Solution:

We have,

x^2-x\sin x-\cos x=0

for any positive root in

(-∞,∞)

f'(x)=2x-\sin x-x \cos x+\sin x=0

⇒2x-x \cos x=0

⇒x(2-\cos x)=0

\cos x=2

[which is not possible]
Hence, number of root will be zero.

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