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Algebra FormulasAlgebra Formulas "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #3 20060402 23:13:38
Re: Algebra FormulasA quadratic equation consists of a single variable of degree 2 and is of the form The roots of the equation are given by Two roots or solutions are obtained, but sometimes they may be equal. If the discriminant b²4ac>0, the roots are real and distinct. If b²4ac=0, the roots are real and equal. If b²4ac<0, the roots are distinct and imaginary. The sum of the roots = b/a Product of the roots = c/a Given the roots of the quadratic equation, the quadratic can be formed using the formula x²(sum of the roots)x + (product of the roots)=0. Character is who you are when no one is looking. #4 20060405 01:52:24
Re: Algebra FormulasI. Arithmetic Progressions. The sum of n terms of an AP, Sn is given by the formula or where l is the last term (nth term in this case) of the AP. Character is who you are when no one is looking. #5 20060405 01:58:16
Re: Algebra FormulasII. Geometric Progression where a is the first term and r is the common ratio. The nth term of a Geometric Progression is given by The sum of the first n terms of a Geometric Progression is given by (i) When r<1 (ii) When r>1 Sum of the infinite series of a Geometric Progression when r<1 Geometric Mean (GM) of two numbers a and b is given by Character is who you are when no one is looking. #6 20060407 00:09:05
Re: Algebra FormulasHarmonic Progression: The Harmonic Mean (HM) of two numbers a and b is The Harmonic Mean of n nonzero numbers is Relation between Arithmetic Mean (AM), Geometric Mean (GM) and Harmonic Mean (HM) that is, AM, GM, HM are in Geometric Progression. For two positive numbers, AM ≥ GM ≥ HM equality holding for equal numbers. For n nonzero positive numbers, AM ≥ GM ≥ HM Character is who you are when no one is looking. #7 20060407 00:28:14
Re: Algebra FormulasSUMMATION Character is who you are when no one is looking. #8 20060419 01:45:51
Re: Algebra FormulasLaws of Exponents In all the above cases, where a is a nonzero real number. and n is a nonnegative number. If a is a postive real number and m,n are integers with n positive, If and b are positive real numbers and n a natural number, then If , then a=b. If then m=n. Character is who you are when no one is looking. #9 20060504 00:22:33
Re: Algebra FormulasBinomial theorem where Summation of Binomial coefficients If n is a rational index and 1<x<1, then Some expansions: Character is who you are when no one is looking. #10 20060511 02:05:40
Re: Algebra FormulasExpansions of Logarithmic expressions Character is who you are when no one is looking. #11 20060512 01:48:23
Re: Algebra FormulasAP, GP, HP : Some important results For example, let the two numbers be 4 and 16. The AM of the two numbers is 10 and their GM is 8. Therefore, A=10, G=8 gives two values, viz. 16 and 4. If are in Geometric Progression, then are in Arithmetic Progression. Similarly, if are in Arithmetic Progression, then are in Geometric Progression. Character is who you are when no one is looking. #12 20060514 22:52:28
Re: Algebra FormulasArithmeticoGeometric Series In the above example, the third term is[a+2d]r², i.e.2. The sum of the series to n terms is In the series given above, the sum of the first four terms would be 20+[(1/2)(7/8)][1/4]7(1/16)/(1/2)=207/47/8=2021/8=139/8. It can be seen, 10+9/2+2+7/8=(80+36+16+7)/8=139/8. The sum to infinity, Character is who you are when no one is looking. #14 20070301 15:13:49
Re: Algebra FormulasThis is all very handy to a 4th grade teacher who took calculus only 25 short years ago! My current problem is to find out a formula for what another web site calls a "triangular number" pattern. 1, 3, 6, 10, 15 . . . Strength and Honor #15 20070301 15:25:48
Re: Algebra FormulasHi MissK, They form a series of numbers which are the sum of the first n natural numbers. Character is who you are when no one is looking. #16 20070301 23:00:16
Re: Algebra FormulasTriangular Numbers: Definition of Triangular Number "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #17 20070302 14:25:08
Re: Algebra Formulas
Oh  Oops! Sorry. That means I can only write brilliant formulas. OK Strength and Honor #18 20070308 19:20:03
Re: Algebra Formulas'im learning a lot here Zappzter  New IM app! Unsure of which room to join? "ZNU" is made to help new users. c: #19 20070510 13:01:55
Re: Algebra FormulasAn example of figurometry formulas: #20 20080419 10:53:12
Re: Algebra Formulas(a+b)^c = sum starting at k=1 to infinity((v choose k) x^k a^(vk)) I couldn't get that to work in LaTeX. Linux FTW #21 20090103 02:06:20
Re: Algebra FormulasComponendoDividendo which is called the componendo. If , then, which is called dividendo. If , then, which is called the componendo & dividendo. Character is who you are when no one is looking. #22 20090111 00:30:24
Re: Algebra Formulas1. 2. If a+b+c = 0, 3. (i) is divisible by (xa) for all values of n. 3. (ii) is divisible by (x+a) for all even values of n. 3.(iii) is divisible by (x+a) for all odd values of n. Character is who you are when no one is looking. #24 20090111 01:51:39
Re: Algebra FormulasThis is also useful. And this. (slightly different from Ganesh’s formula) #25 20091125 05:18:43
Re: Algebra FormulasI learned limits today!!!! 