SOLUTION: Find a polynomial f(x) of degree 3 that has the following zeros. 7,0,-5, Leave your answer in factored form.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial f(x) of degree 3 that has the following zeros. 7,0,-5, Leave your answer in factored form.       Log On


   

Question 1127287: Find a polynomial f(x) of degree 3 that has the following zeros. 7,0,-5, Leave your answer in factored form.
Found 3 solutions by Boreal, KMST, Edwin McCravy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
a zero of a polynomial is the factor (x-c), where c is the root
(x-7)(x)(x+5)=f(x)

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A polynomial of degree 3 can have up to 3 real zeros.
The factored form of polynomial f(x) will include %28x-a%29 if and only if a is a zero of f%28x%29 .

so, highlight%28f%28x%29=%28x-7%29x%28x%2B5%29%29
is a polynomial f(x) of degree 3 that has the zeros 7,0,-5.
There can be no zeros other than those 3 zeros,
so there can be no other factors involving x .
Equivalent expressions, such as f%28x%29=x%28x-7%29%28x%2B5%29 are really the same polynomial.
Expressions involving a constant such as
f%28x%29=2x%28x-7%29%28x%2B5%29 or f%28x%29=pi%28x-7%29x%28x%2B5%29
are also polynomials that could be valid answers.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
zeros:  7,0,-5,

f%28x%29+=+%28x-7%5E%22%22%29%28x-0%5E%22%22%29%28x-%28-5%29%5E%22%22%29

f%28x%29+=+%28x-7%29%28x%29%28x%2B5%29  <-- in factored  form

f%28x%29+=+%28x%5E2-7x%29%28x%2B5%29

f%28x%29+=+x%5E3%2B5x%5E2-7x%5E2-35x

f%28x%29+=+x%5E3-2x%5E2-35x

Edwin