Ask Question
8 December, 13:01

Determine how many zeros, how many real or complex, and find the roots for f (x) = x3 - 5x2 - 25x + 125.

+2
Answers (1)
  1. 8 December, 15:46
    0
    We can write this as:-

    P (x) = + x^3 - 5x^2 - 25x + 125

    There are 2 changes of real sign so by Descartes Rule of signs there are either 2 positive real roots or 0 positive roots.

    P (-x) = - x^3 - 5x^2 + 25x + 125

    There is just one change of sign so there is exactly 1 real negative root.

    125 is a multiple of 5 so By rational root theorem 5 could be a positive root.

    P (5) = 125 - 125 - 125 + 125 = 0 so one zero is 5

    if we divide the polynomial by (x - 5) we get the quadratic

    x^2 - 25

    (x + 5) (x - 5) = 0

    x = 5,-5

    so the roots are 5 (multiplicity 2) and - 5.

    2 real positive zeroes and one real negative zero
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Determine how many zeros, how many real or complex, and find the roots for f (x) = x3 - 5x2 - 25x + 125. ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers