Before using a theorem, make sure the assumptions are met to show that the function p(x) = x* + 4x³ – 9 has two real roots, that is, there exist r1, r2 ER such that rị # r2 and p(r1) = 0 = p(r2). Let...

Extracted text: Before using a theorem, make sure the assumptions are met to show that the function p(x) = x* + 4x³ – 9 has two real roots, that is, there exist r1, r2 ER such that rị # r2 and p(r1) = 0 = p(r2). Let f:X→R be a Lipschitz continuous function defined on X. Show that f is uniformly continuous on X.