Question

If one zero of polynomial 2x^3+x^2-7x-6 is 2 then find all zeroes

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Answer 1

2,-1 and -3/2

Explanation:

If one zero of polynom is 2 then we can divide our polinom with (x-2), and we will get

(2x^3+x^2-7x-6)/(x-2)=2x^2+5x+3

Now we have ti find zeros for 2x^2+5x+3

3 is without x so we have factors:

1,-1,3,-3, 1/2,-1/2,3/2,-3/2.

Chack does any of them zero.

For -1 we have:

2(-1)^2+5(-1)+3=2-5+3=0

So -1 is zero of the polynom.

Now divide again with (x+1) wi get:

(2x^2+5x+3)/(x+1)=2x+3

2x+3=0 if x=-3/2

So we have all zeros:

2,-1 and -3/2