Find a polynomial of degree 3 that has zeros, 1, -2, and 3, and in which the coefficient of x^2 is 3?

1 Answer
Feb 2, 2018

f(x) = -3/2x^3+3x^2+15/2x-9

Explanation:

Each zero a corresponds to a linear factor (x-a).

So we can write a monic cubic polynomial with the required zeros by multiplying as follows:

(x-1)(x+2)(x-3) = x^3-2x^2-5x+6

Then to make the coefficient of x^2 into 3, multiply by -3/2 to get:

f(x) = -3/2x^3+3x^2+15/2x-9