Question

Find the rational solution of x^3-3x^2+x+5=0. Show your use of the rational zero theorem to receive credit.

Answer 1

The rational root (or zero) theorem says a polynomial's rational zeros must have factors of the constant in the numerator and those of the leading coefficient in the denominator.

Here the leading coefficient is 1 and the constant is 5, so our only possibilities for rational roots are 1, -1, 5, -5

We try them each in term

1-3+1+5=6 nope

-1 -3 -1 +5 = 0 yes, x = -1 is a rational zero

5 and -5 don't work either so we're left with

Final answer: x = -1