Polynomial Zeros

Form a polynomial whose zeros are: 1, 2, -2 and has a degree of 3.


Anyone know how to do this ?


Thanks

Quote:

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Originally Posted by jwaingold

Form a polynomial whose zeros are: 1, 2, -2 and has a degree of 3.


Anyone know how to do this ?


Thanks

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This isn't as bad as you think. What does having a zero of a function mean? It means that inputting a certain value will output zero for the function. Let's say we have a quadratic with zeros of 2 and 3. In factored form, you could say that the zeros could be expressed by x-2 and x-3. If you wanted to put them together you could write it like (x-2)(x-3). Do you see how 2 and 3 are zeros? Now apply this same logic to your question.

but what does the degree of 3 part mean ?

degree of three means that the polynomial will look like this

a*x^3 + b*x^2 + c*x + d

the highest power of x is the degree.

to get your answer you will do something like this:

(x-a)*(x-b)*(x-c) when you multiply it all out you will get the degree three polynomial you are looking for.

Jwain pm'd me and still doesn't see the answer so I will explain it further.

polynomial is degree three and zeros are: 1, 2, -2

meaning that when x = 1, 2, or -2, y=0

the answer will start from the form of

y=(x-a)*(x-b)*(x-c) where y = zero when x = a, b, or c

does that make sense? let us substitute x=a

y=(a-a)*(a-b)*(a-c)
y=(0)*(a-b)*(a-c)
y=0

now we know the zeros are 1, 2, and -2 so the solution will look like this:

y=(x-1)*(x-2)*(x-(-2))

now simply multiply out the three terms and you will get your polynomial.