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 $a^{2}+b^{2}-ab.$