Question

if 2 and -2 are two zeros of the polynomial 2x^4-5x^3-11x^2+20x+12,find all the zeros of the given polynomial​.

Answer please...

Answer 1

Answer:

Since degree of polynomial is 4, there will be 4 zeroes.

If 2 and -2 are two zeroes, then there will be two factors (x+2) and (x-2). We have to find out two more factors

(x+2)(x-2)= x^2-4

Now divide the polynomial 2x^4-5x^3-11x^2+20x+12 by (x^2-4)

you will get 2x^2-5x-3 now factorise this by mid term splitting

you will get (2x+1)(x-3)

Take 2x+1=0 gives x=-1/3

and x-3=0 gives x=3

So all the zeroes of the polynomial are

2,-2,-1/3 and 3