#1238 · Algebra · Quadratics

Difference of roots invariance

If the roots of the equation $a x^{2} + 2 b x + c = 0$ are $α$ and $β$ , and those of the equation $A x^{2} + 2 B x + C = 0$ are $α + δ$ and $β + δ$ , prove that $\frac{b ^{2} - a c}{a ^{2}} = \frac{B ^{2} - A C}{A ^{2}}$ .

~10 minProof · checked by AIDiscriminantRoots of quadratic equations

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.b, No. 9

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