A) \[p\in (-\pi ,0)\]
B) \[p\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]
C) \[p\in (0,\pi )\]
D) \[p\in (0,2\pi )\]
Correct Answer: C
Solution :
Given equation \[(\cos p-1){{x}^{2}}+(\cos p)x+\sin p=0\] Its discriminant \[D\ge 0\] since roots are real Þ \[{{\cos }^{2}}p-4(\cos p-1)\sin p\ge 0\] Þ \[{{\cos }^{2}}p-4\cos p\sin p+4\sin p\ge 0\] Þ \[{{(\cos p-2\sin p)}^{2}}-4{{\sin }^{2}}p+4\sin p\ge 0\] Þ \[{{(\cos p-2\sin p)}^{2}}+4\sin p(1-\sin p)\ge 0\] ?..(i) Now \[(1-\sin p)\ge 0\] for all real p, \[\sin p>0\]for \[0<p<\pi .\] Therefore \[4\sin p(1-\sin p)\ge 0\] when \[0<p<\pi \]or \[p\in (0,\pi )\]
You need to login to perform this action.
You will be redirected in
3 sec
