#1221 · Algebra · Quadratics

Difference of roots squared ratio

If $α$ , $β$ are the roots of the equation $a x^{2} + b x + c = 0$ , find the value of $(\frac{α}{β} - \frac{β}{α})^{2}$ .

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H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.a, No. 20

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).