Question

Find the value of $\theta$, if the equation $\cos \theta x^2-2\sin \theta x-\cos \theta =0$ has real roots

• A. $-\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $-\frac{\pi }{3}$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (A), (B), (C), (D)

$\frac{\pi }{4}$

Discriminant $=4(-2\sin \theta {)}^2-4\times \cos \theta \times (-\cos \theta \left)\right)$

$=16{\sin }^2\theta +4{\cos }^2\theta$
$=4({\sin }^2\theta +{\cos }^2\theta )+12{\sin }^2\theta$
$=4+12{\sin }^2\theta$
$\Rightarrow △>0$
$\Rightarrow$ Given equation has real roots for all value of $\theta$