Beyond the Basics

115. $- 2 \sqrt{3} or 2 \sqrt{3}$ $- 2 \sqrt{3} or 2 \sqrt{3}$
117. 0 or 8
121. 2
123. $\begin{array}{l} a x^{2} + b x + c = a x^{2} - a (r + s) x + a r s = a (x^{2} - r x - s x + r s) \\ = a [x (x - r) - s (x - r)] = a (x - r) (x - s) \end{array}$ $\begin{array}{l} a x^{2} + b x + c = a x^{2} - a (r + s) x + a r s = a (x^{2} - r x - s x + r s) \\ = a [x (x - r) - s (x - r)] = a (x - r) (x - s) \end{array}$
125.
1. $x^{2} - x - 12 = 0$ $x^{2} - x - 12 = 0$
2. $x^{2} - 10 x + 25 = 0$ $x^{2} - 10 x + 25 = 0$
3. $x^{2} - 6 x + 7 = 0$ $x^{2} - 6 x + 7 = 0$

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Table of Contents for Beyond the Basics