Question

If -1 and 2 are the 2 zeros of the polynomial 2 x cube minus x square minus 5 x minus 2 find its third zero

Answer 1

zeroes of the ppolynomial are:
x=-1 
x=2
therefore,
x+1=0
x-2=0
(x+1)(x-2)
x^2-2x+x-2
x^2-x-2
by dividing x^2-x-2 by the polynomial 2x^3-x^2-5x-2
we get the quotient 2x+1
then, 2x+1=0
2x=-1
x=-1/2
hence the third zero is -1/2

Answer 2

let,p(x)=2x^3-x^2-5x-2

if -1and 2are zeros of p(x) then

(x+1) and(x-2) are factors of p(x)
consequebtly,(x+1)(x-2)=(x^2-x-2) is factor of p(x)

On dividingp(x) by x^2-x-2;we get

p(x)=(x^2-x-2)(2x+1)
p(x)=(x+1)(x-2)(2x+1)

Hence,p(x)=0
(x+1)(x-2)(2x+1)=0

(x+1)=0 or (x-2)=0 or (2x+1)=0
x=-1 x=2 x=-1/2

Hence,the 3rd zero is -1/2