exercise 16.JPlease prove EVERYTHING, (if they affirm something, please prove it even if it seems easy) 16.J. Show that every polynomial of odd degree and real coefficients has areal root. Show that the polynomial p(x) = x* + 7x³ – 9 has at least tworeal roots.16.K. If c > 0 and n is a natural number, there exists a unique positive num-ber b such that b*с.16.L. Let f be continuous on I to R with f(0) < 0 and f(1) > 0. If N ={x € I: f(x) < 0}, and if c16.M. Let f be a continuous function on R to R which is strictly increasing inthe sense that if x' < x" then f(x') < f(x"). Prove that f is one-one and that itsinverse function f- is continuous and strictly increasing.sup N, show that f(c)0.

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Answered: 16.J. Show that every polynomial of odd…

16.J. Show that every polynomial of odd degree and real coefficients has a real root. Show that the polynomial p(x) = x¢ + 728 – 9 has at least two real roots. -

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

exercise 16.J

Please prove EVERYTHING, (if they affirm something, please prove it even if it seems easy)

16.J. Show that every polynomial of odd degree and real coefficients has a
real root. Show that the polynomial p(x) = x* + 7x³ – 9 has at least two
real roots.
16.K. If c > 0 and n is a natural number, there exists a unique positive num-
ber b such that b*
с.
16.L. Let f be continuous on I to R with f(0) < 0 and f(1) > 0. If N =
{x € I: f(x) < 0}, and if c
16.M. Let f be a continuous function on R to R which is strictly increasing in
the sense that if x' < x" then f(x') < f(x"). Prove that f is one-one and that its
inverse function f- is continuous and strictly increasing.
sup N, show that f(c)
0.

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