SOLUTION: describe how to find the polynomial from the following roots: 0,0,3,-3 step by step

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Question 1068311: describe how to find the polynomial from the following roots: 0,0,3,-3
step by step
Found 2 solutions by Fombitz, Boreal:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The roots mean that the polynomial has factors,
f%28x%29=%28x-a%29%28x-b%29%28x-c%29%28x-d%29
Substitute for the values of a,b,c,d.
f%28x%29=%28x-0%29%28x-0%29%28x-3%29%28x-%28-3%29%29
f%28x%29=x%28x%29%28x-3%29%28x%2B3%29
f%28x%29=x%5E2%28x%5E-9%29
f%28x%29=x%5E4-9x%5E2

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
root of 0 is factor x.
When there are two roots of 0, the factor is x^2
root of 3 means factor (x-3), because x-3=0 gives root 3
root of -3 means factor (x+3)
(x+3)(x-3)x^2 are the factors
x^2(x^2-9)=0;
x^4-9x^2=0
Note, a repeated root "bounces" off the x-axis.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E4-9x%5E2%29