Question

obtain all the zeores of the polynomial x4-17x2-36x-20 if two of its zeroes are 5 and-2

Answer 1

as the degree of the equation is 4 the total no. of zeroes will be 4

now, we will obtain a quadratic equation with the help of the zeroes given

either X=5 or X=-2  

x-5=0 or x+2=0

(x-5)(X+2)=0

X2-5X+2X-10=0

X2-3X-10=0

the quadratic equation obtained will be a factor of the given polynomial.

now simply divide

x4-17x2-36x-20/x2-3x-10

the quotient obtained will be a quadratic equation.

the zeroes of that equation will be the zeroes of the given polynomial also.