Question

The number of points of intersection of two curves $y=2\sin x$ and $y=5x^2+2x+3$ is

• A. $0$
• B. $1$
• C. $2$
• D. infinitely many

Answer 1

The correct option is A $0$

Number of points of intersection of curves $y=f\left(x\right)=2\sin x$ and $y=g\left(x\right)=5x^2+2x+3$ is same as the number of solutions of $f\left(x\right)=g\left(x\right)$
$\Rightarrow 2\sin x=5x^2+2x+3$
L.H.S. $\le 2$ and
R.H.S. $\ge \frac{-(4-60)}{20}$
R.H.S. $\ge \frac{56}{20}$
R.H.S. $\ge 2.8$
So, there is no solution