Question

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

Answer 1

Solution:

we have been asked to find the potential roots of the function

$f(x) = 5x^3-7x + 11$

using rational root theorem.

Here the constant term is 11 with factors 1 and 11 and the leading coefficients is 5 with factors 1 and 5.

So the potential roots of the given function as per the rational root theorem is

$\pm\frac{1,11}{1,5} =\pm\frac{1}{1,5} ,\pm\frac{11}{1,5}=\pm\frac{1}{1} ,\pm\frac{11}{1}\pm\frac{1}{5} ,\pm\frac{11}{5}\\\\\\\text{Hence the potential roots are }\\\\\pm1,\pm11,\pm\frac{1}{5},\pm\frac{11}{5}$

Answer 2

Make a set of fractions where the numerator is the factors of the constant term and the denominators are factors of the leading coefficient

±11/±5. or 11/5, -11/5