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Relation between Roots and Coefficients for Quadratic

If α and β ar...

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If α and β are the roots of the quadratic equation x^2 – 5x + 2 = 0, then a quadratic equation whose roots are α/β and β/α can be

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α, β

are roots of the quadratic equation

x^{2} - x - 1 = 0,

then the quadratic equation whose roots are

\frac{1 + α}{2 - α}, \frac{1 + β}{2 - β}

Q. A quadratic equation, whose roots are

α

β

can be written as

(x - α) (x - β) = 0 = x^{2} - (α + β) x + α β

a x^{2} + b x + c \equiv a (x - α) (x - β)

α

β

are the roots of the equation

x^{2} - p x + q = 0

, then find the quadratic equation with the roots

(α^{2} - β^{2}) (α^{3} - β^{3})

α^{3} β^{2} + α^{2} β^{3}

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