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Modulus Function

If Alpha and ...

Question

If Alpha and beta are the roots of quadratic equation ax²+bx+c=0 , then write Alpha ⁵+ beta⁵.

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α, β

are the roots of quadratic equation

a x^{3} + b x + c = 0

, then find the value of

\frac{α}{β} + \frac{β}{α}

α, β

are the roots of the equation

a x^{2} + b x + c = 0

then the quadratic equation whose roots are

α + β, α β

Q. In the quadratic equation

a x^{2} + b x + c = 0, Δ = b^{2} - 4 a c a n d α + β, α^{2} + β^{2}, α^{3} + β^{3},

are in G.P. where

α, β

are the root of

a x^{2} + b x + c = 0,

α

β

are the roots of

a x^{2} + b x + c = 0

, then the quadratic equation whose roots are

\frac{1}{α}

\frac{1}{β}

α

β

are roots of the quadratic equation

a x^{2} + b x + c = 0

. The equation has real roots which are of opposite signs, then the equation

α (x - β)^{2} + β (x - α)^{2} = 0

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