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Difference between revisions of "1981 AHSME Problems/Problem 28"

(Created page with "==Problem 28== Consider the set of all equations <math> x^3 + a_2x^2 + a_1x + a_0 = 0</math>, where <math> a_2</math>, <math> a_1</math>, <math> a_0</math> are real constants...")
(No difference)

Revision as of 21:15, 13 August 2019

Problem 28

Consider the set of all equations $x^3 + a_2x^2 + a_1x + a_0 = 0$, where $a_2$, $a_1$, $a_0$ are real constants and $|a_i| < 2$ for $i = 0,1,2$. Let $r$ be the largest positive real number which satisfies at least one of these equations. Then

$\textbf{(A)}\ 1 < r < \dfrac{3}{2}\qquad \textbf{(B)}\ \dfrac{3}{2} < r < 2\qquad \textbf{(C)}\ 2 < r < \dfrac{5}{2}\qquad \textbf{(D)}\ \dfrac{5}{2} < r < 3\qquad \\ \textbf{(E)}\ 3 < r < \dfrac{7}{2}$

Solution

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