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

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Solution

The correct option is A
0

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

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y = 2 sin x

y = 5 x^{2} + 2 x + 3

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