Thread: anyone know a quick way to find the zeroes to a polynomial function?

if the function is 2x^3-9x^2+22x-30, there are many possible zeroes but to find all the zeroes that work for the function, it takes a long time to try all those possible zeroes through synthetic division. anyone know a quicker way?

Originally Posted by ss103

if the function is 2x^3-9x^2+22x-30, there are many possible zeroes but to find all the zeroes that work for the function, it takes a long time to try all those possible zeroes through synthetic division. anyone know a quicker way?

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Originally Posted by ss103

if the function is 2x^3-9x^2+22x-30, there are many possible zeroes but to find all the zeroes that work for the function, it takes a long time to try all those possible zeroes through synthetic division. anyone know a quicker way?

Descartes rule of signs tells us this has 1 or 3 positive roots, and 0 negative roots. So if this has any rational roots the rational root theorem tells us they are amoung 1, 2, 3, 5, 6, 10, 15, 30, 1/2, 1.5, 2.5, and 7.5. Of these only 2.5 is a root.

Factor out (x-2.5) and you are left with a quadratic factor to deal with.

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