SOLUTION: Find a polynomial function f with real coefficients that satisfies the given conditions. degree 4; zeros − 1/2, 2, −i; f(−1) = 282

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial function f with real coefficients that satisfies the given conditions. degree 4; zeros − 1/2, 2, −i; f(−1) = 282      Log On


   

Question 1095478: Find a polynomial function f with real coefficients that satisfies the given conditions.
degree 4; zeros − 1/2, 2, −i; f(−1) = 282
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
If a+bi is a solution of a polynomial, then a-bi is also a solution. That means that the roots of our polynomial are -1/2, 2, -i, and i.

(Here, a is a constant.)

a(x + 1/2)(x - 2)(x - i)(x + i)
a(x + 1/2)(x - 2)(x^2 + 1)
a(x^4 - 3x^3/2 - 3x/2 - 1) = y

Plug in the point (-1, 282) to find the value of a, then you can find the polynomial.