Samsonite 528 Report post Posted November 28, 2005 So I had my exam-like test today and after doing some parts of a task I suddenly came to a stop: What do I do if this happens? I can't get that number to appear in small just above and to the right of a number, so I do this instead: something(2) = something*something 3x(2)-11x = 24 I had a little problem with that... Can you guys tell me what to do in such situations? Thank you! 0 Share this post Link to post Share on other sites
cleves 148 Report post Posted November 28, 2005 Well, you transfer the 24 to the other side and create this3x^2-11x-24=0Then you use Cubic equation to solve it:(-b+-root(b^2-4*a*c))/2aAnd you should get 2 answers of this equation. 0 Share this post Link to post Share on other sites
dawidjoubert 161 Report post Posted November 28, 2005 Ill explain..What you see there is a quadratic equation, and it should have been handled fully at your school, and they should teach you how to solve it using A: FormulaB: FactorisationC: Completion of the SquareFirst lets get it in the STANDARD quadratic equation form which is "ax^2 + bx + c = 0"THEN PLEASE NOTE That quadratics always have 2 answers, and sometimes you get a repeated answer in which case both answers are just the same, however not all of the answers are REAL NUMBERS and so the others we will ignore :-)3x(2)-11x = 24 ----> 3x^2 - 11x + 24 = 0// Now not every single quadratic can be solved by factorisation so the formula as samsonite gave you is-----------------------First Answer/First Root ________ -b + _/ b*b - 4acx = --------------------------------- 2aSecond Answer/Second Root ________ -b - _/ b*b - 4acx = --------------------------------- 2aAs you see the sign infront of the square root just changed which is why the formala will be written with a +- sign on top of each other....Now Completion of the Square is a variation on the vactorisation it involves an advanced method of factorisation (*which is how the formula was originally worked out*)if we have the quadratic in this shapeax*x + bx+c = 0then we re-arrane to getx*x + bx/a = -c/aAnd now we add (bx/a)*(bx/a) to both sides so we getx*x + bx/a + (b/2a)^2 = -c/a + (b/2a)^2Now we can factorise the left side like this(x + b/2a)^2 = -c/a + b^2/4a^2which gives ______________ __________________/(x + b/2a)^2 =_/ -c/a + b^2/4a^2which becomes ________________x =_/ -c/a + b^2/4a^2 - b/2a// Consider that which is under the Square root-c/a + b^2/4a^2 can become (b^2-4ac)------------ 4a^2// Which leaves ----------------x =_/ (B^2 - 4ac) ---------- - b/2a 4a^2and finaly we can take 4a^2 up one by sqr rooting it ----------------x =_/ (B^2 - 4ac) * 2a - b/2aCommon de-numerators ----------------x = -b + _/ (B^2 - 4ac) ------------------- 2a And logic says that a square root can be either + or - and so thats why it really is ----------------x = -b +-_/ (B^2 - 4ac) ------------------- 2a Hope thats not 2 much theory for one night 0 Share this post Link to post Share on other sites
Mike2343 1202 Report post Posted November 28, 2005 Quote:Original post by dawidjoubert3x(2)-11x = 24 ----> 3x^2 - 11x + 24 = 0It's actually 3x^2 - 11x - 24 = 0 0 Share this post Link to post Share on other sites
deavik 570 Report post Posted November 28, 2005 Quote:Original post by SamsoniteI can't get that number to appear in small just above and to the right of a number, so I do this instead:Just for reference [smile], use plain html: < sup>superscript here</sup > -> ^{superscript here}Looks like your other question has been comprehensively answered. [smile] 0 Share this post Link to post Share on other sites
nilkn 960 Report post Posted November 28, 2005 To summarize on what has already been said:An equation which is of the form ax^{2} + bx + c = 0 where a, b and c are constants drawn from an algebraic field (typically the complex numbers) is called a quadratic equation because it is a second-order polynomial. Note that "of the form" is a precise mathematical term meaning, in this case, that your equation does not need to be in that form initially, only that it can be put into that form. Your equation, therefore, is of that form.For solving quadratic equations you use the quadratic formula:An alternative form is You may also rest assured that because quadratics are second-order polynomials that the fundamental theorem of algebra guarantees two solutions in the field of complex numbers (which contains the real numbers as a subfield).[Edited by - nilkn on November 28, 2005 8:02:57 PM] 0 Share this post Link to post Share on other sites
dawidjoubert 161 Report post Posted November 28, 2005 nilkn i see you gave an alternative formula.. COOL.. i didnt know theres another shape to it.Is there more alternatives? 0 Share this post Link to post Share on other sites
Boku San 428 Report post Posted November 28, 2005 This won't help you anymore. Well, it might help with memorization...just a bit.We learned quadratic formula with a song -- "X equals opposite b, plus or minus the square root of (b squared minus four-a-c), all over two-a."...Ok, so it's not much of a song, and it doesn't have much rhythm, but say it enough times and you won't forget it. 0 Share this post Link to post Share on other sites
dawidjoubert 161 Report post Posted November 29, 2005 Quote:Original post by Boku SanThis won't help you anymore. Well, it might help with memorization...just a bit.We learned quadratic formula with a song -- "X equals opposite b, plus or minus the square root of (b squared minus four-a-c), all over two-a."...Ok, so it's not much of a song, and it doesn't have much rhythm, but say it enough times and you won't forget it.Lol, hahaha thats the cutest thing i have ever heard!!No thanks i am well adept at memorizing it. But thanks 0 Share this post Link to post Share on other sites
nilkn 960 Report post Posted November 29, 2005 Quote:Original post by dawidjoubertnilkn i see you gave an alternative formula.. COOL.. i didnt know theres another shape to it.Is there more alternatives?Heh, actually I wasn't even aware there was an alternative form. I got the images of the formula from MathWorld, and they had an alternative form listed, so I thought I might as well post it. [smile] 0 Share this post Link to post Share on other sites
grhodes_at_work 1385 Report post Posted November 30, 2005 I'm closing the thread. Folks, homework/schoolwork question are against forum policy! Please review the Forum FAQ. There are OTHER sites on the web that are appropriate for schoolwork (see the FAQ), but gamedev is not a place to ask general schoolwork questions! 0 Share this post Link to post Share on other sites