Algebra
# Polynomial Inequalities

**possible** that Romeo's ratio of correct solutions to attempted problems will be **strictly greater than** Juliet's.

\[ x^{2} + ax+a^{2} + 6a <0\]

Find the sum of squares of all integral values of \(a\) for which the inequality above is satisfied for all \(1<x<2.\)

Consider the function \(f(x)=\dfrac{x^{2}+ax+b}{x^{2}+2x+3}\) where \(a\) and \(b\) are positive integers.

If the range of \(f(x)\) is \([-5,4],\) find the value of \(a^{2}+b^{2}-ab.\)

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