JEE problem

Algebra Level 3

Find number of real roots for the equation

P.S: Better if you can give a solution by using calculus. (Hint: Check points where curve is increasing or decreasing)

1 0 2 3

1 solution

Naman Kapoor
May 10, 2015

If there is a change in sign of the value of f(x) then one root will be lying between them

Here

When ,

          x=0.     f(x)=-1

          x=-1.    f(x)=15

          x=-2.    f(x)=85

          x=-3.     f(x)=293

After that the value of f(x) will be positive when we decrease x

Now taking ,

           x=1.      f(x)=9

           x=2       f(x)=9

           x=3.      f(x)=83

After that the value of x will be positive if we increase x

At two places there was a sudden change in sign when x=0,x=1 and x=0,x=-1 so there are only two real solutions lying one lying between 0 and 1 other lying between 0 and -1

Hence the ans is $\boxed{2}$

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