Try this beautiful problem from TOMATO Objective no. 258 based on Real Roots of a Cubic Polynomial.

**Problem: Real Roots of a Cubic Polynomial **

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 * f(x)* 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 .

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