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August 13th, 2017, 07:09 AM  #1 
Newbie Joined: Aug 2017 From: Bath, UK Posts: 4 Thanks: 0  The Discriminant
Firstly would you would say that this comes under Linear or Abstract Algebra? If I've posted it in the wrong place sorry. I have been confuddled by this question. Find the range of values of a for which the following equations have two real roots: ax^2 + 2x +3 = 0 I've given it a couple of goes, but can't seem to get the correct answer. See attached for my scruffy workings. If someone could just show me how they would work through the problem then I will probably be able to see where I am doing wrong. Many thanks 
August 13th, 2017, 07:15 AM  #2 
Senior Member Joined: Oct 2009 Posts: 139 Thanks: 56  
August 13th, 2017, 07:27 AM  #3 
Newbie Joined: Aug 2017 From: Bath, UK Posts: 4 Thanks: 0 
Hi Micrm@ss Yes I realised that after posting. I'm from the UK so we use the wrong words for things. And thank you. You may not realise it but you just pointed out to me what I was doing wrong. b^24ac I was putting 4(a*c) meaning that everything was being multiplied by 4 as opposed to just multiplying them together. User error. Thanks again. 
August 14th, 2017, 07:24 AM  #4 
Newbie Joined: Aug 2017 From: Bath, UK Posts: 4 Thanks: 0 
Right, after realising what I was doing wrong I could get the correct answers for a couple of questions. But not this one: X2 + 8x + a =0 D = 8^2 – 4 * 8 * a = 0 D= 64 – 32a = 0 Divide by 32: D = 2 – a = 0 Which would mean that the answer is a < 2 But the answer is apparently a < 16. What am I doing wrong? Many thanks 
August 14th, 2017, 07:46 AM  #5  
Math Team Joined: Jul 2011 From: Texas Posts: 2,598 Thanks: 1287  Quote:
for $y = x^2 + 8x + a$ ... note that $a$ is the constant $c$ and $1$ is the leading coefficient, $a$, in the above equation for the discriminant, $D$ suffice to say, $a$ was a poor choice to represent the constant term. $D = 8^2  4 \cdot 1 \cdot a = 644a = 0 \implies a = 16$  
August 14th, 2017, 07:48 AM  #6 
Newbie Joined: Aug 2017 From: Bath, UK Posts: 4 Thanks: 0 
Thanks Skeeter.

August 14th, 2017, 07:55 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra  

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