Problem 260: Find the other two roots of the polynomial
if is a root.
Solution: Since we are given one of the roots, we can use root to set up a binomial term as follow:
One can now use this binomial and long division to find a quadratic polynomial which we know how to solve.
That is, set up the problem as a long division problem.
The quotient of this long division is . Now, all we have to do is factor the quadratic polynomial or use the Quadratic Formula and solve for .
Using the quadratic formula, we found the second and third roots.
Thus, the third degree polynomial has roots at .
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