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]}