Question

if alpha and beta are zeroes of quadratic polynomial ax²+bx+c=0 then evaluate 1/alpha+1/beta-2alphabeta
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Answer 1

Answer:

Ax² + bx +c =0

zeroes α,β

sum of roots = α+β = -b/a

products of roots = αβ = c/a

1/α - 1/β = β-α / αβ   ............(1)

β-a = √(b² - 4ac/a² )      putting this value

1/α - 1/β  = √(b²-4ac/a²)  / c/a   =  √b²-4ac / c

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