Question

If -1 and 2 are two zeroes of the polynomial 2x 3 -x 2 -5x-2 find its third zero.

Answer 1

If -1 and 2 are zeroes, then the factor will be
(x+1)(x-2) = x² -2x+x -2 = x² - x -2

Now, to find the third factor, dividing the given equation with this factor,

x²-x-2 )2x³-x² -5x -2( 2x+1
           2x³-2x²-4x
         -     +    +
           0    x²-x-2
                 x²-x-2
                -  + +
                0   0 0

so, 2x³-x² -5x -2 =(x²-x-2)(2x+1)

The third factor will be 
(2x+1) = 0
⇒x = -1/2

Answer 2

Answer:

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