Find the roots of the function f(x) = x3 + x2 + 6x 

We will use the concept of factorization to find the roots of the above function.

Answer: The roots of the function f(x) = x3 + x2 + 6x  are 0 , -3 , -2

Let us see how we will use the concept of factorization to find the roots of the above function.

Explanation:

For the equation  x3 + x2 +  6x , lets take a common factor x from the equation .

The resultant equation becomes x ( x2 + x + 6 ) .

Now factorizing the quadratic equation ( x2 + x + 6 ) .

The above quadratic equation can be written as x2 + 3x + 2x + 6 [ splitting the middle term ]

Now taking a common factor x from the first part of the quadratic equation i.e. x2 + 3x and taking a common factor 2 from the second part of the quadratic equation 2x + 6 we get the resultant equation that is x ( x + 3 ) + 2 ( x + 3 ).

Now using the distributive property we collect the common terms and the quadratic equation becomes ( x + 2 ) ( x + 3 ) 

Thus, the overall function can be written as x ( x + 2 ) ( x + 3 ) 

On equating all the three different factors separately with 0 we got 0, -2, and -3 as the roots.

Roots of the function x3 + x2 + 6x = 0 are 0 , -2 , -3

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