Question

Find the rational roots of the following: \)3x^3-5x^2+15x-25=0\)

Answer 1

• possible: ±{1/3, 1, 5/3, 5, 25/3, 25}
• actual: 5/3

Explanation:

The rational root theorem tells you any rational roots of the expression will be found from the constant and the leading coefficient:

rational roots = ±{divisor of 25} / {divisor of 3}

Possible roots

The list of divisors in each case is pretty short, so this is ...

rational roots = ±{1, 5, 25) / {1, 3} = ±{1/3, 1, 5/3, 5, 25/3, 25}

Actual roots

We find the only actual rational root is x = 5/3 when we graph the function.

(Factoring out that root, we find the remaining roots are ±i√5, irrational imaginary values.)