SOLUTION: How do I form a polynomial whose zeros and degrees are given Zeros: 9, multiplicity 1; 2, multiplicity 2; degree 3

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Question 1203999: How do I form a polynomial whose zeros and degrees are given
Zeros: 9, multiplicity 1; 2, multiplicity 2; degree 3

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52924) About Me  (Show Source):
You can put this solution on YOUR website!
.

Polynomial  P(x) = %28x-9%29%2A%28x-2%29%5E2  has the degree 3 and zeroes 9, multiplicity 1 and 2, multiplicity 2.    ANSWER



    How to create such a polynomial ? - Nothing is easier than it.


        Take linear binomials with assigned zeros; raise each such a binomial into 
        a degree equal to the corresponding multiplicity, and multiply these polynomial factors.

Solved.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Zeros: 9, multiplicity 1; 2, multiplicity 2; degree 3
using zero product formula, function of degree 3 is:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 where x%5B1%5D, x%5B2%5D, and x%5B3%5D+ are zeros
given that
x%5B1%5D=9+
x%5B2%5D=2 multiplicity 2 which means third zero is same, so
+x%5B3%5D=2

f%28x%29=%28x-9%29%28x-2%29%28x-2%29+
f%28x%29=%28x-9%29%28x-2%29%5E2
f%28x%29=x%5E3+-+13x%5E2+%2B+40x+-+36

+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+x%5E3+-+13x%5E2+%2B+40x+-+36%29+