If - and - are zeroes of polynomial a x 2-b x-c then find 1 - a -b-1 - a -b

Given that equation ax^2 + bx + c = 0 has roots α and β = gt; α + β = b/a and αβ = c/a /(aα + b) + 1/(aβ + b) We already know that α + β = b/a = gt; a ...

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Standard X

Mathematics

Formation of a Quadratic Equation From It's Roots

if α and β ar...

Question

if α and βare zeroes of polynomial ax2+bx+c then find 1/aα+b + 1/aα+b

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Solution

Given that equation ax^2 + bx + c = 0 has roots α and β

=> α + β = -b/a
and αβ = c/a
/(aα + b) + 1/(aβ + b)

We already know that
α + β = -b/a
=> a(α + β) = -b
=> -a(α + β) = b

Substituting this value of b in the problem,

=> 1/(aα + b) + 1/(aβ + b)
=> 1/(aα - a(α + β)) + 1/(aβ - a(α + β))
=> 1/(-aβ) + 1/(-aα)
=> -1/a (1/β + 1/α)
=> -1/a (α + β)/αβ
=> -1/a (-b/a)(c/a)
=> b/ac

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