Question

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

• A. 0
• B. 1
• C. 2
• D. $\infty$

Answer 1

Answer: (A)

Given, $y=2\sin x$
and $y=5x^2+2x+3$
$=5\left(x^2+\frac{2}{5}x\right)+3$
$\Rightarrow y-3=5\left(x^2+\frac{2}{5}x+\frac{1}{25}-\frac{1}{25}\right)$
$\Rightarrow y-3=5{\left(x+\frac{1}{5}\right)}^2-\frac{1}{5}$
$\Rightarrow y-3+\frac{1}{5}=5{\left(x+\frac{1}{5}\right)}^2$
$\Rightarrow 5{\left(x+\frac{1}{5}\right)}^2$
$=y-\frac{14}{5}$
$\Rightarrow {\left(x+\frac{1}{5}\right)}^2$
$=\frac{1}{5}\left(y-\frac{14}{5}\right)$

Here, we see that two curves do not intersect any point
Hence, no solution exist