Question

Obtain all zereos of the polynomial f(x) x^4+x^3-34x^2-14x^2-19x-6 if two of zereos are given -3,-2

Answer 1

sum of the zeroes = -3+-2= (-5)
product of the zeroes =-3*-2=6

x^2-(sum of the zeroes(x) + product of the zeroes)
=x^2-(-5)x+6
=x^2+5x+6 is a factor

x^2+5x+6/x^4+x^3-48x^2-19x-16

and then after dividing you will get a quotient

and then you have to split the middle term of quotient and you will get the zeroes