find all the zeroes of the polynomial 2x^4+5x^3-11x^2-20x+12 if two of its zeroes are 2 and -2
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Since two zeroes are 2 and -2, (x-2)(x+2)=x^2-4 must be a factor. Algebraic long division gives us:

            2x^2+5x-3 = (2x-1)(x+3) so the other zeroes are 1/2 and -3.

x^2-4 ) 2x^4+5x^3-11x^2-20x+12

            2x^4           -8x^2

                     5x^3  -3x^2-20x

                     5x^3           -20x

                               -3x^2       +12

                               -3x^2       +12

                                        0

 

                              

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