Question

What is the correct ratio of each rational root of the polynomial function: f(x) = 5x5 − x3 + 3x + 6? a)factor of 6/5 b) factor of 6/1 c) factor of 4/factor of 6 d) factor of 6/factor of 5

Answer 1

The correct ratio of each rational root of the given polynomial function is a factor of 6/factor of 5.

Step-by-step explanation:

The polynomial function is given as f(x) = 5x5 - x3 + 3x + 6. We are looking for the correct ratio of each rational root of the function. In order to find the rational roots, we can use the Rational Root Theorem. According to the theorem, if there is a rational root, it will be of the form p/q, where p is a factor of the constant term (6) and q is a factor of the leading coefficient (5).

So, the correct ratio of each rational root of the polynomial function is a factor of 6/factor of 5, which corresponds to option d.

Answer 2

The correct poynomial function should be f(x) = 5x^2 − x^3 + 3x + 6. The factors are  x1 = 5.7095, x2 = -0.35475 + i * 0.96179 x3 = -0.35475 - i * 0.96179. The roots are composed of two imaginary roots and one real root. There is no correct ratio that can be made as there are alrady imaginary roots