How do you write a polynomial in standard form given the zeros x=-1/2,0,4?

1 Answer
May 28, 2016

Answer:

You multiply #x# minus the solution and you obtain #x^3-7/2x^2-2x=0#.

Explanation:

The solutions of a polynomial are those numbers that assigned to the #x# gives zero. So the easiest way to construct the polynomial from the solutions is to multiply together #x# minus the solution because you are sure that it becomes zero.
In our case we have

#x-(-1/2)#
#x-0#
#x-4#

It is clear that the three of them become zero when x is, respectively #-1/2#, #0# and #4#. If we multiply the three we have

#(x+1/2)x(x-4)#

we have a polynomial that will become zero for #-1/2#, #0# and #4# because these three numbers set as zero one of the three factors and the product for zero is zero, no matter what are the other factors.

Now it is just a multiplication to do to obtain the final result

#(x+1/2)x(x-4)#
#=(x+1/2)(x^2-4x)#
#=x^3-4x^2+1/2x^2-2x#
#=x^3-7/2x^2-2x#

and the corresponding equation is

#x^3-7/2x^2-2x=0#.