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).
Solution Preview
Let the equation f(x) = 0 where
F(x) = xn + p1xn-1 + p2xn-2 + ..........+ pn
If α1,α2,......,αn are the roots of f(x) = 0
then
xn + p1xn-1 + p2xn-2 + .......+ pn ≡ (x - ...
Solution Summary
This solution is comprised of a detailed explanation for the relation between roots and coefficients. It contains step-by-step 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 step-by-step explanation.