Question

If $0<p<\pi$, then the quadratic equation, $(\cos p-1)x^2+x\cos p+\sin p=0$ has real roots.
If true enter $1$ else enter $0$.

Answer 1

$(\cos p-1)x^2+x\cos p+\sin p=0$
Here, $D={\cos }^{2}p-4\sin p(\cos p-1)$
$D={\cos }^{2}p+4\sin p(1-\cos p)$
$D={\cos }^{2}p+8\sin p{\sin }^2\frac{p}{2}$
Since, $0<p<\pi$
$\Rightarrow 0<\sin p<1$
Clearly $D>0$
Hence, the given quadratic equation has real roots