Find all zeros of the polynomial P(x)=x3−3x2−9x−5. Its zeros are x1= , x2= and x3= with x1≤x2≤x3.

Answer 1

Guess one solution or root by checking some small easy numbers. -1 is a root so you need to divide (Long Division) the original polynomial by X-(-1) which is X + 1. So:

X^3 - 3X^2 - 9X - 5

--------------------------- = X^2 - 4X - 5 Now if we solve by quadratic formula or factoring we will have:

X + 1

X ^2 -4X - 5 = (X - 5)(X + 1) = 0 so X1 = 5 and x2 = 1

So the original polynomial has two roots or zeros of -1 and one root of +5. So X1 = -1, X2 = -1 and X3 = 5.