• # question_answer The number of points of intersection of the two curves$y=2\sin x$ and $y=5{{x}^{2}}+2x+3$ is    [IIT 1994] A)            0      B)            1 C)            2      D)            $\infty$

Put $y=2\sin x$in $y=5{{x}^{2}}+2x+3$Þ$2\sin x=5{{x}^{2}}+2x+3$ Þ $5{{x}^{2}}+2x+3-2\sin x=0$                               .....(i) $x=\frac{-2\pm \sqrt{4-20(3-2\sin x)}}{10}$. It is clear that number of intersection point is zero, because $0\le \sin x\le 1$ and in all the values roots becomes imaginary.