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The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.

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The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.

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Let α and β be the roots of the quadratic equation. According to the given conditions,

∴ The required quadratic equation is

x2 – (α + β)x + αβ = 0 

∴ x – 5x + 6 = 0

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