Question

If two zeroes of the polynomial x4+3x3-20x2-6x+36 are square root2 -Square root2.find the other zeroes of the polynomial

Answer 1

zeroes= root2 and -root2
(x-root2) (x+root2)              [a^2 - b^2= (a+b) (a-b)]
therefore,
=x^2 - root2^2
=x^2 - 2 == g(x)
p(x) = x^4+3x^3-20x^2-6x+36
 then divide p(x) and g(x) using long division method , i.e
p(x) / g(x)
after dividing you will get an linear equation. either by splitting the middle term , completing the square or any other relevent method 
you will get 2 answers for x 
that 2 ans are the two other zeroes of polynomial given below