Question

The number of points of intersection of the two curves y = 2sinx and y = 5x² + 2x+3 is

• A. 0
• B. 1
• C. 2
• D. ∞

Answer 1

Answer: (A)

0

Answer 2

Put y = 2sinx in

y = 5x² + 2x + 3 ⇒ 2sinx = 5x² + 2x + 3

⇒ 5x² + 2x + 3 – 2sinx = 0..... (i)

x = $\frac{- 2 \pm \sqrt{4 - 20(3 - 2\sin x)}}{10}$

It is clear that number of intersection point is zero, because 0≤sinx≤1 and in all the values roots becomes imaginary.