# How do you find the zeros of the polynomial function #f(x) = x^3 + x^2 -42x#?

##### 2 Answers

Jun 8, 2018

#### Explanation:

To start, every term has an

What I have in blue can be factored by a thought experiment. What two numbers have a sum of

After some trial and error, we arrive at

We can leverage the zero product property here, setting all three terms equal to zero. As our zeroes, we get

Hope this helps!

Jun 8, 2018

#### Explanation:

**METHOD 1 : Try and Error Method**

We can find out the zeros (roots) of the polynomial. by the '**Try and Error**' method. In this method, we prefer to substitute the integer in given polynomial and wait for zero.

But, this is not fair and good method.**METHOD 2 : Observation Method**

This method is based on observation. In some questions we can apply this. It is important to click this method.

By observation, it is cleared that#x=0# is one of the roots.

#:.# #f(x)=x[x^2+x-42]#

Now, we have to find out the roots of the quadratic equation#x^2+x-42# . It is easier one.

#:.# #f(x)=x[x^2+x-42]#

#:.# #f(x)=x[x^2+7x-6x-42]#

#:.# #f(x)=x[x(x+7)-6(x+7)]#

#:.# #f(x)=x(x-6)(x+7)#

Hence,#x=0# ,#x=6# and#x=-7# are the roots of#f(x)# .**METHOD 3 : Graph Method**

We can draw rough sketch of the graph of#f(x)# with the help of Calculus.

graph{x^3+x^2-42x [-8.89, 8.88, -4.444, 4.445]}