Question

Obtain all the zeros of the polynomial 2x4+x3-14x2-19x-6 if two of it zeroes are -2 and 1
explain step by step

Answer 1

Let the polynomial p(x)
Given zeroes of p(x) are -2,-1
So (x+2)(x+1) is factor of p(x)
So x2+3x-2 is factor of p(x)
Now divide x2+3x-2 with p(x)=2x4+x3-14x2-19x-6
We get q(x)=2x2-5x-3
It is a quadratic equation so by splitting the midle term we get (2x+3)(x-1)=0
Now either 2x+3 =0 or x-1=0
X=-3/2 or x=1
So zeroes are -1,-2,-3/2,1