#1228 · Algebra · Quadratics

Form equation with modified roots

If $α, β$ are the roots of $a x^{2} + b x + c = 0$ , form the equation whose roots are $α^{2} + β^{2}$ and $α^{- 2} + β^{- 2}$ .

~10 minAnswer checked instantlyquadratic equationsVieta's formulassum and product of roots

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.a, No. 28

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