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Relation between Roots and Coefficients for Quadratic

Alpha and bet...

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Alpha and beta are roots of an equation x^2=x+7. Prove that 1/alpha=(alpha -1)/7

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α, β

are the roots of

x^{2} + 3 x + 4 = 0,

then the quadratic equation whose roots are

α^{3} + 4 α^{2} + 7 α + 7

β^{3} - β^{2} - 8 β - 14

α, β

are the roots of

x^{2} + 3 x + 4 = 0,

then the quadratic equation whose roots are

α^{3} + 4 α^{2} + 7 α + 7

β^{3} - β^{2} - 8 β - 14

α, β, γ

are the roots of

x^{3} - 3 x + 7 = 0

, then the equation whose roots are

α + β - γ, β + γ - α, γ + α - β

α, β

are the roots of the equation

a x^{2} + b x + c

, find the values of
(1)

\frac{1}{α^{2}} + \frac{1}{β^{2}}

α^{4} β^{7} + α^{7} β^{4}

{(\frac{α}{β} - \frac{β}{α})}^{2}

α

β

are roots of equation:

2 x^{2} - 14 x + 7 = 0

. Find the value of

\frac{1}{α} + \frac{1}{β}

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Relation between Roots and Coefficients for Quadratic

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