Difference between revisions of "2016 AMC 12A Problems/Problem 24"
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| + | ==Problem== | ||
| + | There is a smallest positive real number <math>a</math> such that there exists a positive real number <math>b</math> such that all the roots of the polynomial <math>x^3-ax^2+bx-a</math> are real. In fact, for this value of <math>a</math> the value of <math>b</math> is unique. What is this value of <math>b</math>? | ||
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| + | <math>\textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 12</math> | ||
Revision as of 18:32, 5 February 2016
Problem
There is a smallest positive real number 
such that there exists a positive real number 
such that all the roots of the polynomial 
are real. In fact, for this value of the value of is unique. What is this value of ?
