SOLUTION: It would be nice if someone could show me how to solve this problem. Thanks in advance. Find a polynomial equation that has the zeros x= +1,-1 and x= +2,-2 and passes through t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: It would be nice if someone could show me how to solve this problem. Thanks in advance. Find a polynomial equation that has the zeros x= +1,-1 and x= +2,-2 and passes through t      Log On


   

Question 21998: It would be nice if someone could show me how to solve this problem.
Thanks in advance.
Find a polynomial equation that has the zeros x= +1,-1 and x= +2,-2 and passes through the point (3,5). Some blanks may contain zeros.
f(x)=(___)X­^4+(____)X^3-(____)X^2+(____)X+(____)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Zeroes at +-1 implies a factor of (x^2-1)
Zeroes at +-2 implies a factor of (x^2-4)
EQUATION:
y = k(x^2-1)(x^2-4)
We need to find "k".
We have a point: when x=3, y=5.
Substitute that values in to get:
5 = k(9-1)(9-4)
5 = k(8)(5)
k = 1/8
The equation you want is y = (1/8)(x^2-1)(x^2-4)
Multiply that out to get
y = (1/8)[x^4-5x^2+4]
y = (1/8)x^4 = (5/8)x^2 +(1/2)
Cheers,
Stan H.