Conic Sections Question 374
Question: The number of points of intersection of the two curves $ y=2\sin x $ and $ y=5x^{2}+2x+3 $ is
[IIT 1994]
Options:
A) 0
B) 1
C) 2
D) $ \infty $
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ y=2\sin x $ in $ y=5x^{2}+2x+3 $
therefore $ 2\sin x=5x^{2}+2x+3 $
therefore $ 5x^{2}+2x+3-2\sin x=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\le \sin x\le 1 $ and in all the values roots becomes imaginary.
BETA
