Question

Math help! *10 points!* Polynomials and Zeros?

I have the answers to these two problems in the back of the book, but I need to know HOW to do them. PLEASE help :)

*Find a polynomial function that has the given zeros:*

4, -3, 3, 0

and

*Find a polynomial of degree "n" that has the given zeros:*

(Zeros are -5, 0, 1) and (Degree is n=3)

Answers

(x-4)(x+3)(x-3)(x-0)

x^4 -4 x^3 -9 x^2 +36 x

(x+5)(x)(x-1) = x^3 +4 x^2 - 5 x

#1

Since you have the zeros already you can easily find the function by going backwards from the zeros.

say:

X=4 subtract 4

X-4=0

X=-3 subtract -3

X+3=0

X=3 subtract 3

X-3=0

X=0 subtract 0

X-0=0 => X=0

now multiply those 4 equations to get the function.

f(X)=X(X-4)(X+3)(X-3)

that would be the function with those zeros.

same thing with this problem

X=-5

X+5=0

X=0

X=1

X-1=0

again multiply the zeros out

f(x)=X(X+5)(X-1)

expanding the function we get

f(x)=X^3 + 4X^2 - 5X

hope that helps

#2