Answer :
Final answer:
In this particular polynomial function, the possible rational roots are 0, 1, -1, 5, -5, 7, -7, 35, -35.
Explanation:
To solve the equation f(x) = 35x^5 + 173x^4 – 118x^3 – 5x^2 and find its real zeros, we need to factor the polynomial function.
By factoring, we can set the polynomial function equal to zero and find the values of x that make it true. We can start by factoring out the greatest common factor, if any. In this case, there is no common factor other than 1.
Next, we can look for rational roots using the Rational Root Theorem. The possible rational roots of a polynomial are the factors of the constant term divided by the factors of the leading coefficient. In our function, the constant term is 0, and the leading coefficient is 35. Therefore, the possible rational roots are all factors of 0 divided by all factors of 35 (including both positive and negative values).
Upon finding one rational root, we can use long division or synthetic division to divide the function by the linear factor (x – r).
In this particular polynomial function, the possible rational roots are 0, 1, -1, 5, -5, 7, -7, 35, -35. We can test each of these values to see if they are roots of the polynomial function. By using the rational root theorem, we can determine the actual roots of polynomial function f(x). We find that the rational root x = 0 is a root. By using long division or synthetic division, we can further factor the polynomial f(x) to find the remaining roots.
Learn more about Solving Polynomial Equations here:
https://brainly.com/question/14837418
#SPJ11
