October 27th, 2016, 10:43 PM  #1 
Newbie Joined: Oct 2016 From: Toronto Posts: 1 Thanks: 0  Quadratics
Hey, I was just wondering about this math problem. Given the parabola y=ax^2+bx+9, find the values of a and b if the parabola passes through the point (8,1) and ax^2+bx+9=0 has two equal roots. If anyone could solve this problem it would be great!

October 27th, 2016, 11:00 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,755 Thanks: 900 
$y=ax^2 + b x + 9$ $(8,1 ) \Rightarrow 1 = a(8 )^2 + b(8 ) + 9 = 64a + 8b +9$ $8 = 64a + 8b$ $1 = 8a + b$ 2 equal roots $\Rightarrow (b^2  4(a)(9))=0$ $b^2 = 36a$ I leave it to you to solve these two equations for $a,~b$ 
October 28th, 2016, 02:46 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,557 Thanks: 1480 
It's impossible for a quadratic to have two equal roots. When its discriminant is zero, a quadratic has just one root, sometimes called a repeated root or a root of multiplicity 2 (because the quadratic's factorization contains a linear factor that is repeated or raised to the power of 2).

October 28th, 2016, 03:08 AM  #4  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
first sentence in different words. The two roots are one and the same. The roots are equal to each other. The roots coincide with one another. Etc. They're just different ways of looking at it/describing it. Last edited by skipjack; October 28th, 2016 at 04:10 AM.  
October 28th, 2016, 04:40 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,557 Thanks: 1480 
If the discriminant is zero, there is just one root, not two roots that coincide or are the same. The phrases "repeated root" and "root of multiplicity 2" are not ideally worded, but would seem lengthy and clumsy if changed to "root corresponding to a repeated linear factor" and "root corresponding to a squared linear factor".

October 28th, 2016, 02:38 PM  #6  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
the same [root]" mean it's a repeated root. "Two roots that coincide" mean that they have become one [root]. You have difficulty (or are stubborn) with the English to mathematics, in my opinion.  
October 28th, 2016, 06:08 PM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,664 Thanks: 653 Math Focus: Wibbly wobbly timeywimey stuff. 
Please agree to disagree. You are arguing semantics here. Dan 
October 29th, 2016, 04:04 PM  #8 
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 468 Thanks: 40 
I'm going to agree with @skipjack. Love his impartiality and ruthlessness. He's sent me a few brutal replies, but they've kept my feet on the ground. I'm not trying to brown nose here, I'm simply stating an opinion. There's nothing wrong with dealing with semantics. They can help us clarify our thoughts. Mind you, I did find this on the internet: b2  4ac = 0 can someone briefly explain thanks  The Student Room You may like to read it. 

Tags 
quadratics 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Help please with quadratics  Paul9999  Algebra  2  April 15th, 2015 02:31 PM 
quadratics  jessjans11  Algebra  3  August 18th, 2014 07:19 AM 
quadratics  grangeeducation  Algebra  1  April 10th, 2014 10:12 AM 
Quadratics  sallyyy  Algebra  3  June 4th, 2011 02:58 AM 
Quadratics Help  maria186  Algebra  1  February 10th, 2010 06:34 PM 