Question

If two zeroes of the polynomial x4+3x3-20x2-6x+36 are√2 and –√2, find the other zeroes of the polynomial.

Answer 1

p(x) =x4+3x3-20x2-6x+36
x+√2 and x-√2 are the factors of p(x)
then (x+√2)(x-√2) = x2- 2 is also the factor of p(x) on dividing p(x) by x2-2 we get x2+3x-18 as quotient then we factorise it and get (x-3)(x+6)=+3,-6