Let p denote the quadratic polynomial defined by p(t) = at
Chapter 1, Problem 25E(choose chapter or problem)
Problem 25E
Let p denote the quadratic polynomial defined by p(t) = at +bt2 + c, where a, b, and c are real numbers. Use Rolle’s theorem to prove the following: If t0, t1; and t2 are real numbers such that t0 <t1<t2 and if p(t0)= 0, p(t1) = 0, and p(t2)= 0, then a = b = c =0. (Recall that Rolle’s theorem states there are values u1 and u2 such that w, is in (t0, t1) u2 is in (t1, t2), p’(u1) = 0 and p’(u2) = 0.)
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