My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 16th, 2015, 03:20 PM   #1
Member
 
Joined: Apr 2014
From: Missouri

Posts: 39
Thanks: 1

Finding of the constant term for the function to have distinct root

Hi

I was solving this question.

The function f(x)=x^3-12x+k has three distinct roots if and only if k is strictly between a and b. Find |a-b|

Now in the solve they assumed that the function have 2 distinct roots and then they solve it and find the value of a and b (the range of k).

Then they use this value as the final answer. How come two root is same as three root when the question clearly stated distinct root?

Thanks and Regards
Shen is offline  
 
January 17th, 2015, 05:57 AM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

If a cubic equation has all three roots "distinct" then it is certainly true that any two of them are distinct.
Country Boy is offline  
January 19th, 2015, 10:33 AM   #3
Member
 
Joined: Apr 2014
From: Missouri

Posts: 39
Thanks: 1

Hi country boy

The solution looked like this. They assumed that it has two distinct root p & q. so the equation should be (x-p)*(x-p)*(x-q)=0 and given x^3-12x+k=0 so

2p+q=0, p^2+2pq=-12 and p^2q=-k. Buy solving first two we can get values of p &q and replacing them in equation 3 we will get two different values of k.

Now the solution said as k is in between a (-16 in this particular case) and b(16 specifically) so the difference is 32. Now the whole solve was done for two root. I'm confused in this portion. How two root solve is true for 3 root?

Last edited by Shen; January 19th, 2015 at 10:34 AM. Reason: partially written message posted
Shen is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
constant, distinct, finding, function, root, term



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Prove analytic function is constant, if argument is constant ag07 Complex Analysis 6 December 4th, 2015 08:05 PM
find the constant term when (1+x^2)(x-(3/x))^4 rhubarb123 Algebra 2 May 16th, 2014 10:38 PM
Q Constant term kingkos Algebra 4 December 20th, 2012 12:51 PM
Ordered distribution of distinct objects into distinct conta metamath101 Algebra 2 June 22nd, 2012 05:59 PM
Finding the next term fe phi fo Algebra 1 June 4th, 2012 02:21 PM





Copyright © 2018 My Math Forum. All rights reserved.