Purchase Solution

Roots of x3 + 3px2 + 3qx + r = 0 in H.P.=>2q3 = r(3pq - r).

Not what you're looking for?

Ask Custom Question

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).

Purchase this Solution

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.

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


xn + p1xn-1 + p2xn-2 + .......+ pn ≡ (x - ...

Solution provided by:
  • BSc, Manipur University
  • MSc, Kanpur University
Recent Feedback
  • "Thanks this really helped."
  • "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
  • "Very nice thank you"
  • "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
  • "You are awesome. Thank you"
Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.