## Question

The maximum number of real roots of the equation 2*x*^{88} + 3*x*^{87} − 13*x*^{2} + 5*x* + 9 = 0 is

**Joshi sir comment**

2*x*^{88} + 3*x*^{87} − 13*x*^{2} + 5*x* + 9 = 0

implies that 2*x*^{88} + 3*x*^{87} = 13*x*^{2} - 5*x* - 9

or *x*^{87}(2x+3*)* = 13*x*^{2} - 5*x* - 9

now plot the left and right graphs for getting the intersecting points

Hint: Parabola will face in upward direction as a is positive, take x=0 we get -9 so 1 root will be positive and 1 negative,

*x*^{87}(2x+3*) *will be 0 for x = -3/2 and x = 0 besides it consider some values as x = 1 and -1

You will get one root between 0 and -1

now check both the graph at x= -2, you will get the idea about the second intersection