Wednesday, September 5, 2012

α & β are roots of ax^2+bx+c=0 a,b,c real constants & λ is a constant find equation with roots α+ λ and β+ λ?

α & β are roots of f(x) = ax^2+bx+c=0

so α+ λ and β+ λ are root of f(x - λ)

the reason is x = α+ λ => x - λ = α and x = β + λ => x - λ = β

f(x) = ax^2+bx+c=0
=> f(x - λ) -= a (x - λ)^2 + b(x - λ) + c = 0

or ax^2 + x(b- 2a λ) + (c- bλ+ aλ^2) = 0

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