Roots of x3 + 3px2 + 3qx + r = 0 in H.P.=>2q3 = r(3pq  r).
Theory of Equation
Relation between Roots and Coefficients
Harmonical Progression
Arithmetical Progression
Problem : If the roots of x3 + 3px2 + 3qx + r = 0 are in Harmonical Progression, show that 2q3 = r(3pq  r).
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Let the equation f(x) = 0 where
F(x) = xn + p1xn1 + p2xn2 + ..........+ pn
If α1,α2,......,αn are the roots of f(x) = 0
then
xn + p1xn1 + p2xn2 + .......+ pn ≡ (x  ...
Solution Summary
This solution is comprised of a detailed explanation for the relation between roots and coefficients. It contains stepbystep explanation to show that if the roots of x3 + 3px2 + 3qx + r = 0 are in Harmonical Progression, then 2q3 = r(3pq  r). Notes are also given at the end. Solution contains detailed stepbystep explanation.
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