Question

If pxsquared+qx+q=0,prove square root ofa÷b+square root of b÷a+square root of q÷p=0
how to solve it?

Answer 1

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