Question

if -1 and 2 are two zeroes of the polynomial p(x)=2x³-x²-5x-2, find the third zeroes​

Answer 1

Step-by-step explanation:

Given that

p(x)=2x³-x²-5x-2

The two zeroes are -1 and 2.

So (x+1) and (x-2) are the factors of p (x).

=> (x+1)(x-2)=x²-x-2 is a factor of p ( x)

Now p (x)=2x³-x²-5x-2

=2x³-2x²-4x+x²-x-2

=2x(x²-x-2)+1(x²-x-2)

=(x²-x-2)(2x+1)

Now 2x+1=0=> 2x=-1=> x=-1/2

Thus the third zero is -1/2.

hope you got it.