* Problem:*Let a,b,c be distinct real numbers.Then the number of real solution of is

(A) **1**

(B)** 2**

(C) **3**

(D) depends on a,b,c

**Solution: Ans: (A)**

Let

But it is not possible a quadratic equation has three roots.so, it implies that * f'(x)* has no real roots.But

**is a cubic polynomial. And we know a cubic polynomial must have at least one real root ( we know all polynomial curves are continuous ,so it cuts either of the axes at least once).So, number of real root of the given equation is 1 .**

*f(x)*