If a and b be the roots of equation px^2+qx-q=0 show that √(a/b)+√(b/a)-√(q/p) =0
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Let α and β are the roots of given equation px² + qx + q = 0
sum of roots = α + β = -q/p --------(1)
product of roots = αβ = q/p -------(2)
Given, ratio of roots = a/b
α/β = a/b --------(3)
multiply equations (2) and (3)
αβ × α/β = q/p × a/b = qa/pb
α² = qa/pb
taking square root both sides,
α =
put this in equation (2)
β = q/pα = q/p√{aq/pb} =
Now, put it in equation (1)
α + β = -q/b
Hence , proved//
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