Ask Question
15 April, 07:35

Show that p (x) = 2x^3 - 5x^2 - 10x + 5 has a real root.

+3
Answers (1)
  1. 15 April, 07:38
    -1
    All odd degrees polynomials with real coefficients have (at least) a real root, and are continuous. This is because the curve goes diagonally and must pass through the x-axis.

    The above polynomial can be evaluated at x1=-10 and x1=+10 (or any other large enough number)

    f (-10) = - 2395

    f (10) = 1405

    Since they have opposite signs, the function must intersect the x-axis between x1 and x2 by the intermediate value theorem, hence there is (at least) one root.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Show that p (x) = 2x^3 - 5x^2 - 10x + 5 has a real root. ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers