If α and β are the zeros of a x² + b x + c = 0, and γ and δ are the zeros of l x² + m x + n = 0, then the equation whose roots are α + βδ and αδ + βγ is

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a² l² x² - abmx + b² l n + acm² - 4acln = 0. For roots (alpha*gamma+beta*delta) and (alpha*delta+beta*gamma): their sum = (alpha+beta)(gamma+delta) = (b/a)(m/l) and product reduces to b^2 l n + a c m^2 - 4 a c l n over a^2 l^2. Forming the monic equation and clearing denominators gives a^2 l^2 x^2 - a b m x + b^2 l n + a c m^2 - 4 a c l n = 0.

If α and β are the zeros of a x² + b x + c = 0, and γ and δ are the zeros of l x² + m x + n = 0, then the equation whose roots are α + βδ and αδ + βγ is

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