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Problem 4 (6 points) Suppose g(x) is a monic polynomial of even degree d, that is g(x) = xd +bd-1xd1 + +6x+bo ... for

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Problem 4 (6 points) Suppose g(x) is a monic polynomial of even degree d, that is g(x) = xd +bd-1xd1 + +6x+bo ... for some real numbers bo, b, ..., bd-1 E R. Suppose 9(0) < 0. Show that g has at least two distinct roots, that is, there exists at least two real numbers c = c2 such that g(C1) g(C2) = 0.

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