Question

given that x-√5 is factor of the polynomial x3-3√5x2-5x+15√5, find all the zeros of the polynomial

Answer 1

given that x-√5 is a factor of the cubic polynomial x3-3√5x2+13x-3√5

            x-√5 ) x3-3√5x2+13x-3√5 ( x2 -2√5x + 3     
                      x3- √5x2  ( substract )
                     -------------------------------
                       - 2√5x2+13x
                       - 2√5x2+10x    ( substract )
                      ------------------------------
                                   3x - 3√5
                                   3x - 3√5    ( substract )
                                  ------------------------
                                        0
∴ The quotient is x2 -2√5x + 3 = 0

Using roots of quadratic formula

a = 1,  b = 2√5,  c = 3

x = (-b ± √(b2 - 4ac) ) / 2a

x = (2√5 ± √((2√5)2 - 12) ) / 2
 
∴ the other zeros are x = √5 ± √2

Answer 2

Answer:

the zeros of the polynomials are -√5,√5 and 3√5

Step-by-step explanation: