# 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).

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:49 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/relation-between-roots-coefficients-equation-13087

#### 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.

$2.49