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You are not logged in. #1 20120925 18:15:19
The three zeros of a polynomialThe two zeros of a polynomial are andand the polynomial is What is the third zero? My approach to such kinds of problem is to divide the polynomial by the two given factors to obtain the other factor and then the zero. Can Someone suggest a quicker and more efficient method? Last edited by Agnishom (20120925 18:16:07) 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20120925 19:43:15
Re: The three zeros of a polynomialI'm not sure what exactly your approach would be. Originally, I just posted my approach: (By polynomial longdivision) Therefore, the other zero is 1 But having reread your first post, I think that might be what you would have done anyway. I'm not sure that I know any more efficient method. But I suggest you just divide once and then factorise, that  at least  might make things a little faster? Last edited by Au101 (20120925 19:46:43) #3 20120925 20:01:08
Re: The three zeros of a polynomialhi Agnishom and Au101 you might notice that which means you know (x+1) is factor straight away by the factor theorem. In general, dividing by known factors is the way. Bob ps. For typical exam questions, they cannot choose factors that would take a long time to find, so I always do a quick mental check for x = +/1, +/2, +/3. If I haven't found a factor by then I do another quicker question first. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #4 20120925 20:20:17
Re: The three zeros of a polynomialSo, Is division the only way? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #5 20120925 21:18:48
Re: The three zeros of a polynomialWell, as you know that cubic = linear x quadratic you can sort of figure out the quadratic coefficients as you go. It takes less time but amounts to short cut division so it's not really a new method. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20120925 22:06:12
Re: The three zeros of a polynomialHi; are equal to So you have this equation to solve solving for r3 you get r3 = 1 which is the third root. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20120927 08:11:25
Re: The three zeros of a polynomialHi bobbym! Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #8 20120927 09:23:16
Re: The three zeros of a polynomialHi noelevans; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20120927 12:48:05
Re: The three zeros of a polynomialHi again bobbym! Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #10 20120927 18:12:32
Re: The three zeros of a polynomialHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 