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Modulus Function

if alpha and ...

Question

if alpha and beta are the roots of equation ax^2+bx+c=0, then write alpha^5+beta^5 in terms of a,b,c.

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α, β

are the roots of the equation

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

, then find the value of

\frac{1}{α^{2}} + \frac{1}{β^{2}}

a, b, c

α

β

are the roots of the equation

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

,express the roots of the equation

a^{3} x^{2} - a b^{2} x + b^{2} c = 0

in the terms of

α

β

α, β

are the roots of the equation

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

\frac{α}{a β + b} + \frac{β}{a α + b} =

α, β

are the roots of

{a x}^{2} + b x + c = 0, (a \neq 0)

α + δ, β + δ

are the roots of the equation

{A x}^{2} + B x + C = 0, (A \neq 0)

for the same constant

δ

Q. In the quadratic equation

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

are in GP where

α, β

are the root of

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

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