
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 16th, 2017, 07:18 PM  #1 
Newbie Joined: Feb 2012 Posts: 19 Thanks: 0  Anyone can find the roots of this quadratic equation?
$\displaystyle 2a^{2}+2b^{2}c^{2}+12bck +19k^{2}2bc\cdot\sqrt{k\cdot\left(4bc+5k\right)}7k\cdot\sqrt{k\cdot\left(4bc+5k\right)}+2a\cdot(2bc5k+\sqrt{k\cdot\left(4bc+5k\right)})=0$ Here a,b,c>0, and a>bc. I want to find the solution of k as a function of (a, b, c). Anyone can help? Thanks. Last edited by loveinla; December 16th, 2017 at 07:28 PM. 
December 16th, 2017, 07:28 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 
I don't think it's quadratic. Have you tried plugging it in to an online CAS (Computer Algebra System), such as Wolfram Alpha?

December 17th, 2017, 07:30 AM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 638 Thanks: 85 
Can a quadratic equation have more than two variables?

December 17th, 2017, 09:04 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,329 Thanks: 1024 
Yikes...one of ugliest equation I've seen! OK; here's a similar "less complicated" ugly one: k^2 + k + sqrt(ak)  sqrt(bk)  sqrt(ck) = 0 Go here to see solutions: http://www.wolframalpha.com/input/?i...k)+%3D+0+for+k Ready to quit?! Last edited by Denis; December 17th, 2017 at 09:09 AM. 
December 17th, 2017, 01:19 PM  #5 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  
December 17th, 2017, 01:19 PM  #6  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
 
December 17th, 2017, 01:31 PM  #7 
Global Moderator Joined: May 2007 Posts: 6,730 Thanks: 689 
The square root expression is the same in all the terms containing it, so it can be factored out. Put the square root containg term on one side of the equation and the rest on the other side. Square both sides and you have a fourth degree polynomial in k.


Tags 
equation, find, quadratic, roots 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
On the Roots of a Quadratic Equation  CapitalSwine  Elementary Math  6  July 11th, 2017 03:33 PM 
how to find the roots of the following quadratic equation?  anup krishna  Linear Algebra  3  August 24th, 2016 04:36 AM 
quadratic equation roots  bongantedd  Algebra  3  February 22nd, 2014 07:10 AM 
Quadratic Equation Ratio of roots  sachinrajsharma  Algebra  1  February 20th, 2013 08:11 AM 
Create a quadratic equation with roots + and  i?3/4  Baseball72Twins  Algebra  2  January 6th, 2012 03:14 PM 