Finding the Roots of a Polynomial Equation

[Mitch885885]

Hello

Question: The polynomial 4x^4 + 24x^3 + kx^2 + px - 15 has roots -1 and -3. Determine any other roots.

I know there are two other roots, due to the degree-4 polynomial, but I am not sure how to locate them, because the value of K and P are unknown. Could the roots -1 and -3 be double roots?

 

[stapel]

You are given roots. By definition, these are zeroes. So plug the two (x, 0) points into the equation, and simplify. This will give you two equations in "k" and "p". Solve the system.

Now that you have the full form of the polynomial, apply synthetic division in the usual manner.

Eliz.