Question

Given that x-root5 is a factor of the polynomial x³-3root5x²+13x-3root5, find all the zeroes of the polynomial.

Answer 1

Given,
x-√5=0
x=√5
Then,
x³-3√5x²+13x-3√5
√5³-3√5*√5²+13*√5-3√5
√5*5*5-3√5*√5*5+13√5-3√5
5√5-3*5√5+10√5
5√5-15√5+10√5
15√5-15√5
0

Hope this helps you!