Does every polynomial have rational zeros? What will happen if we try to use the Rational Zeros Theorem on a polynomial that does not have any rational zeros? (Try it on f(x) = x^2+1)

Answer 1

No, there are polynomials that do not have rational zeros.

If you try to use the Rational zeros theorem on such polynomial, none of the elements, t, in

the set p/q will result in P(t) = 0

x^2+1 --> p = +or-1 and q = +or-1

p/q = +1 or -1

P(1) = 2 and P(-1) =2, so there are no rational solutions...

the equation must be solved numerically , by first examining the graph