How do you find irrational zeros?

Question

I know how to find possible rational zeros p/q and also how to find out if they work as zeros.

But how do you find irrational zeros?

Ex. x^3 + 2x^2 - 4x + 1
rational zeros @ 1

Answer 1

Once you have the rat'l zero; remember, if 1 is a rat'l zero, then (x-1) is a factor of your original poly. Divide your original eqn by (x-1), then use the quadratic formula on what remains, to find any irrational roots.

Answer 2

Divide by x-1 and then you have a quadratic on which you can use the formula.

Thus x^3 + 2x^2 - 4x + 1
=(x-1)(x^2 + 3x -1)
and you probably don't need me to apply the formula.

















But anyway it's
x = (-3 ± √13)/2

Answer 3

Factorize this expression = (x-1)*(x^2+3x-1)
and find the roots of the second factor
x^+3x-1=0 x=((-3+-sqrt(13))/2