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