Question

Find a polynomial of degree 4 that has integer coefficients and zeros 1,-1,2, and 1/2

Answer 1

\[
(x-r_1)(x-r_2)(x-r_3)=0
\]Plugging in the roots here will give you a third degree polynomial.
Then find the the least common denominator of coefficients.

Answer 2

The multiply it all by \(x\) to make it 4th degree.

Answer 3

Just use wio's suggestion, yessi, but add in a fourth root since you have 4 zeros, namely, 1, -1, 2, and 1/2. Multiply it all out and you have your fourth degree polynomial. I would recommend multiplying the first two roots together, since it will make a difference of two squares and will make multiplying the rest of it a little easier.