Question

If ${\cos }^4\theta +\alpha$ and ${\sin }^4\theta +\alpha$ are the roots of the equation $x^2+4x+2=0$, then values of $\alpha$ are

• A. $2$
• B. $-1$
• C. $-2$
• D. None of these

Answer 1

Answer: (D)

None of these

Given, ${\cos }^4\theta +\alpha ,{\sin }^4\theta +\alpha$ are the roots of the equation $x^2+4x+2=0$
Consider,$x^2+4x+2=0$
$\Rightarrow (x+2{)}^2=2$
$\Rightarrow x=-2\pm \sqrt{2}$
$\Rightarrow x=-2+\sqrt{2}or-2-\sqrt{2}$
on comparing with given solutions ${\cos }^4\theta +\alpha ,{\sin }^4\theta +\alpha$.
since $\sin \theta ,\cos \theta$ range as $[-1,1]$.
we can't compare the given solution value with obtained ones.
Hence we can't solve the question.