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

Question

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

1. 0

2. 1

3. 2

4. infinity

Answer 1

1. 0

The first has a value of 0 at (0,0), the second lowest point is at about (0,3)

Answer 2

The answer is   0

Why ?

From the quadratic we have

   x  =  {  -2  +/-   (2^2  -  4 X5X3 )^(1/2)  }  / 2X5

=> x  =  {-2   +/-   ( 4  -  60)^(1/2) }  /  10

=> x  =  {-2   +/-   (imaginary number) } /  10

=> x is an imaginary number

Thus all values of the quadratic are imaginary.



But since the range of y =2sinx only consists of real numbers there can be no points of intersection between these two curves.  

Answer 3

0.

Answer 4

5x² + 2x + 3 has a minimum turning point where x = -2/10 = - 0.2

[This uses the formula x = - b/(2a) for the vertex of the parabola

y = ax² + bx + c

It's a minimum because the coefficient of x² is positive so the graph is concave upwards]

The value of y at this lowest point of the parabola is

5*(-0.2)² -0.4 + 3

= 2.8

The range of 2 sin x is [-2, 2]

and so the two functions can never take the same value,

hence the curves do not intersect.

The first answer, 0, is correct.