SOLUTION: I have to write a polynomial Function using these roots
-1,-1,1
How do I do this??
Algebra.Com
Question 711966: I have to write a polynomial Function using these roots
-1,-1,1
How do I do this??
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
In general, a polynomial that has r as a root will have a factor of (x-r). So the polynomial we are looking for will have factors of:
which simplifies to:
Now all we have to is multiply this out. We can take advantage of the pattern to multiply the first two factors. Or we can take advantage of the pattern to multiply the last two factors. (Remember, with multiplication the order does not matter!) Since the second pattern has a simpler result I'm going to use it to multiply the last two factors:
which simplifies to:
Now we multiply the remaining factors. They do not fit any pattern so we must resort to FOIL:
which simplifies...
Rearranging the terms so they are in standard form:
P.S. When I described the factored form of a polynomial, I left out a minor detail. The general factored form of a polynomial is:
P(x) = a * (x-r) ... (with as many (x-r) factors as there are roots).
The "a" can be any non-zero number and it is the part I left out. The answer we got while ignoring the "a" has, in effect, an "a" of 1. Fell free to re-do the solution and pick a different "a".
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