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. $\infty$

Answer 1

The correct option is A $0$

The first curve is,

$\Rightarrow$ $y=2\sin x$

We know, $-1\le \sin x\le 1\Rightarrow -2\le 2\sin x\le 2$

The second curve is ,

$\Rightarrow$ $y=5x^2+2x+3$

The above equation is quadratic equation.

$\Rightarrow$ $D=b^2-4ac$

$=(2{)}^2-4\times 5\times 3$

$=4-60$

$=-56$

So, $D<0$ and $a=5>0$

Its minimum value $=\frac{-D}{4a}$

$=\frac{-(-56)}{4\times 5}$

$=\frac{14}{5}$

$=2.8$

We can see that, $y$ of second curve is greater than the maximum $y$ of first first curve.

$\therefore$ Curve will not intersect.

$\Rightarrow$ Hence, the number of intersection points are zero.