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P(x) = x^4 - 8p^2/q x^3 + 4qx^2 - 3px + p^2 = 0 4 positive roots

Source: Indian Postal Coaching 2008 set 3 p4

May 25, 2020
algebrapolynomialroots

Problem Statement

Find all real numbersp,qp, q for which the polynomial equation P(x)=x4−8p2qx3+4qx2−3px+p2=0P(x) = x^4 - \frac{8p^2}{q}x^3 + 4qx^2 - 3px + p^2 = 0 has four positive roots.
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