Solve each equation by using the rational root theorem to identify possible roots

Question

Solve each equation by using the rational root theorem to identify possible roots

5x^3 + 27x = 39x^2 - 7

Answer 1

You can use the rational roots theorem, of course, but I would suggest graphing this first.

The possible rational roots are:±1, ±1/5, ±7/5...and the graph will let you pick the right answer.

However, Descartes' rule of signs tells you there can be at most 2 positive real roots and 1 negative real root.

If necessary you can compute the values of the function. Once you find any real root, you can divide it out and find the other 2 using the quadratic formula.