Question

The number of real solutions of the equation $\cos x=x^2+x+1$ is

• A. 2
• B. 1
• C. 0
• D. None of these

Answer 1

The correct option is C 0

$\cos x=x^2+x+1$
$\cos x=x^2+x+1$
$\Rightarrow \cos x={(x+\frac{1}{2})}^2+\frac{3}{4}$
The graphs of $y=\cos x$ and ${(x+\frac{1}{2})}^2+\frac{3}{4}$ do not intersect, so equation has no solution.
$\therefore$ Number of solution is zero