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Thanks Bobbym for your time.
I think I may be having a dyslexic mathematical moment. I knew there there would be 2 roots as X is squared, and can see how that comes about. I'm still slightly puzzled about "taking a factor of 2" do I just divide top and bottom by 2.......I think I'm going for a lie down in a darkened room
Regards ST
Hi Bobbym
The question asks for the answer to be left in surd form
I wondered if you could point me in the right direction on this quadratic equation = 3x²-4x-2=0
I used the formula -b +or -√b²-4ac divided by 2a. I got it down to x=4 _+ 2√10 divided by 6. Now, I cancelled the 2 by 6 getting it to become x= 4=_+ √10 divided 3, thinking this was the lowest form, I checked the answer but I was wrong.
It was given as x= 2_+√10 divided by 3. if you can understand my reasoning and my maths, I can not for the life in me see where (b) became 2 and didn't stay as 4...........help please if you can.
Regards ST
sherpa tensing wrote:]Hello bobbym
Here is the problem that has kept me awake for a few nightsState the minimum value of 2x²-12x+11
This is how the book does it.....it says complete the square and simplify2x²-12x+11 = 2(x²-6x) + 11 (I'm ok so far)
= 2((x-3)² -9) +11 (hmmm? why is -9 not plus 9 when the coefficient of "b" is -6 ie (b/2)²)
=2(x-3²) -7 ..............and where that -7 has come from God only knows......oh! and you bobbym of course?
I can see that when x = 3 that is when y has its minimum value, but how?Can you help please then I can rest easily at night!
Hi ShivamS
I take your point onboard about learning the technique of "completing the square" which i will pursue vigorously. Also I bought a book called Calculus for Dummies (aptly, any good?) where there again it assumes plenty of prior knowledge of the subject, it could be a long job!Hi to you also ganesh thank you for your welcome
Regards Sherpa T
I think the question needs to be stated properly. I think what you are asking is:
Find the minimum y-value of y = 2x^2 -12x + 11
You can solve this in 4 ways. Factoring, completing the square, graphing the parabola or what is usually referred to as "partial factoring." The easiest method is completing the square though.
y = 2x^2 -12x + 11 = 2(x^2 - 6x) + 11 = 2(x^2 -2(3)x + 9 - 9) + 11
Note that x^2 -2(3)x + 9 is a perfect square and therefore can be written as (x-3)^2
y = 2((x-3)^2 - 9) + 11
Now, distribute the 2:
y = 2(x-3)^2 - 18 + 11 =2(x-3)^2 -7 Obviously, the minimum value is -7.As for my opinion on "Calculus for Dummies," I think it is the most ridiculous book in existence. However, if you don't want a rigorous treatment of calculus, then that book is enough to give you a frivolous understanding of the subject - albeit a very bad one. I don't recommend it at all, but of course it's your choice.
Hi ShivamS
I failed completely to, as you say "distribute the 2". When you lay it out, the -9 obviously becomes -18 +11 = -7 Bingo. I only paid £4 for Calculus for Dummies (second hand) so its not the end of the world. I will have a look around for Stewart for Calculus and give it a go. Practice looks like the order of the day for me and being methodical in my working out, meanwhile zzzzzzzzzzzzz
thank you
]Hello bobbym
Here is the problem that has kept me awake for a few nights
State the minimum value of 2x²-12x+11
This is how the book does it.....it says complete the square and simplify
2x²-12x+11 = 2(x²-6x) + 11 (I'm ok so far)
= 2((x-3)² -9) +11 (hmmm? why is -9 not plus 9 when the coefficient of "b" is -6 ie (b/2)²)
=2(x-3²) -7 ..............and where that -7 has come from God only knows......oh! and you bobbym of course?
I can see that when x = 3 that is when y has its minimum value, but how?
Can you help please then I can rest easily at night!
Hi ShivamS
I take your point onboard about learning the technique of "completing the square" which i will pursue vigorously. Also I bought a book called Calculus for Dummies (aptly, any good?) where there again it assumes plenty of prior knowledge of the subject, it could be a long job!
Hi to you also ganesh thank you for your welcome
Regards Sherpa T
Gentlemen?
Thank you so much for your prompt replies.
Firstly in answer to you Bob, yes I have been on your suggested link and found it very informative with integration and differentiation. I write all the formulae down to make it "sink In" and slowly it does.
Secondly to answer you ShivamS last year I bought a Letts Edexcel guide to GCSE Maths question work book and by my standards I sailed through it, bar for things like "sets" and sequences. Suffering from delusions of granduer I have recently bought Letts guide to AS & A2 revision for maths. now, this where mathematics gets serious as you people know. I have had a certain amount of success, but the only problem is the book assumes prior knowlledge of higher level maths, which at the moment my knowledge is limited, but the spirit is very willing and I have the time neccessary. This level will be my limit I think.
Thirdly, Thank you bobbym keep in touch and we'll see how I progress. I have a particular problem with a quadratic equation (not with the formula) but one associated with completing the square. I shall post it tomorrow and If any of you can help me I will be able to sleep at nights. Talking of sleep I'm off now, I need my beauty sleep...........unlike you people.
Good night
Good day to you all
The older I get the more I think of how I should have applied myself at school. My Father always used to say " I wish I could put an old head on young shoulders"......what? but I know what he meant now.! When I became a father myself I tried to help my daughters with their homework, I was ok with the basic stuff but had completely forgotten all about Algebra. I set about to rectfy this when I was 37, I enrolled at the local college for an evening class for GCE/GCSE in mathematics. Well, of course, now I had to apply myself, with 2 daughters on my case and 25 or so teenagers re-sitting the exam. I loved it, I went home after ever lesson, yes!, not to the pub, home, and did my homework like a proper swot. I enjoyed it so much I couldn't wait for the day of the lesson to come around.
I took the exam and got a "C" in the GCE exam and an "A" in the GCSE exam, so feeling quite proud of myself I sat back on my laurels. But now much later in life I've had an idea I might want to teach myself Calculus. Some of it sinks it (very slowly you understand!) but all of it facinates me, So, here I am, please be kind to me, when I put a query on the forum.
Regards Sherpa Tensing
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