ISI2014-DCG-54

Question

The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to

• A. $0$
• B. $1$
• C. $3$
• D. $4$

Comments

Is $4$ the answer??

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@ankitgupta.1729

Any idea how this could be done??

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@`JEET

To make equation satisfy, $cos^2 x +cos^3 x - cos^4 x = 4$ but $-1 \leq cosx \leq +1$. Here, we can't make sum $= 4$ for any real value of $x$. So, no real $x$ exists.

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Thanks.

Answer 1

0 real roots of the equation as the maximum value cos x can take is 1 and then LHS of equation will become 2. LHS can never become 5.