Theory of Equations..  
GENERAL EQUATION OF N^{th} DEGREE Let polynomial f(x) = a_{0}x^{n} + a_{1}x^{n  1} + a_{2}x^{n  2} + ... + a_{n}. where a_{0}, a_{1}, a_{2}, ..a_{n} are rational numbers and n > 0. Then the values of x for which f(x) reduces to zero are called root of the equation f(x) = 0. The highest whole number power of x is called the degree of the equation. For example x^{4}  3x^{3} + 4x^{2} + x + 1 = 0 is an equation with degree four. x^{5}  6x^{4} + 3x^{2} + 1 = 0 is an equation with degree five. ax + b = 0 is called the linear equation. ax^{2} + bx + c = 0 is called the quadratic equation. ax^{3} + bx^{2} + cx + d = 0 is called the cubic equation. Properties of equations and their roots
For example, the equation x^{3} + 4x^{2} + 1 = 0 has 3 roots, The equation x^{5}  x + 2 = 0 has 5 roots, and so onâ€¦
EXAMPLES: I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week. You might also like: Time, Speed and Distance Linear Equations 
Re: Theory of Equations..  
TG , Your article says ...the sum of roots for the eq .
The sum of roots should be = 1 * a1/a0.. Please confirm

Re: Theory of Equations..  
What are you asking Amishe 800? Isn't 1*a1/a0 = a1/a0 ? Its 4.56 am that you have written this. I guess u needed some sleep now yeah? 
Re: Theory of Equations..  
hi tg.please include some more algebra topics like maxima & minima,etc. 
Re: Theory of Equations..  
hey tg in example 2 shouldnt d answer be 5 ..... btw d article is amazing...

Re: Theory of Equations..  
hello sir, i would like to know that in ques no 6, how can u cancel ( x1) on both sides,since it is makin the euation zero(0).

Re: Theory of Equations..  
please give in more chapters on algebra including graphs.. 
Re: Theory of Equations..  
please give in more chapters on algebra including graphs.. 
Re: Theory of Equations..  
sum of roots b/a =2p^21/p(p1) product of roots c/a =p+1/p1 (a+b+c)^2=a^2(1/p(p1))^2 diff of roots for quadratic eq b^2 4ac =a^2(1/p(p1))^2 x= b +(b^2 4ac )^0.5 /2a 
Re: Theory of Equations..  
Hi TG sir, excellent article.... Hoping same for graph theory..Please come up with it. Thanks a lot! 
Re: Theory of Equations..  
Hi TG and others, For example No:4, isn't the answer is none of these. Since the equation, f(x) must have to be equalled to zero at x=any of the roots. i.e f(x)=0 at x=a,b,c if the f(x) is of degree 3, where a,b,c are the roots of the equation f(x). Please correct me if I am wrong. Thanks Jegathiesh.P 
Re: Theory of Equations..  
hi nice smile.. i hv jst joind tg..Can u write original post...i thnk i cn help u..ds is my interest area.. 
Re: Theory of Equations..  
what is â€“ ??????? 
Re: Theory of Equations..  
Fantastic article.. Truly helpful and handy one sir .. Shiva gaurav > negative sign in the overall article is being shown as â€“

Re: Theory of Equations..  
hello everyone how many sign changes are there in x3+x24x+4=0{x3=x raised to the power 3} one or two one from +ve to ve and 2nd from ve to +ve? 
Re: Theory of Equations..  
answer 1 as no. of sign changes on f(x) is 1 
Re: Theory of Equations..  
is the question right ...494 instead of 496 will solve the problem 
Re: Theory of Equations..  
thanx.....it was very helpful 
Re: Theory of Equations..  
Hi TG Sir !!, Another great fan of yours. hats off to you for your tremendous effort. It would really help to hear some of your enlightenments on PROBABILITY 
Re: Theory of Equations..  
Can any one tell me the formula for a^3 +b^3 +c^3 = in eg. 2 
Re: Theory of Equations..  
awwwweeeeeeesome 
Re: Theory of Equations..  
can somebody help me Please explain how to expand (1  x^{9})(1  x^{30}  3x^{10} + 3x^{20})(1  x)^{4} and get the coefficient of x^{11} in this. 
Re: Theory of Equations..  
expansion of (1 + x)n = 1 + nx + n(n  1)x^{2}/2 + n(n  1)(n  2)x^{3}/6 + ... expand (1  x)^{4} this way... 
Re: Theory of Equations..  
Great article... Such a lucid explantion... Ur awesome.. cheers 
Re: Theory of Equations..  
Beautiful.... lucid ... really short of words..... cleared a lot of my doubts..... keep te good wwork 
Re: Theory of Equations..  
In the last question, u cancelled (x1) from both sides which in fact is 0. Isn't this wrong? 
Re: Theory of Equations..  
In last question if we put 1x instead of x then the roots of the equation would be 0,1alpha, 1beta,...... Calculate the product of roots with 9 items that is 10C9=10 
Re: Theory of Equations..  
thnx alot 
Re: Theory of Equations..  
In example 4,option d should be all of these, as the given equation 6x^3 + 5x^2 + 2x + 2=0 can never have a positive root. Am i right moderators? 
Re: Theory of Equations..  
do we have a method to find the general equation of a chord of a given equation of a curve????????????????????????????????????// 
Re: Theory of Equations..  
hi, Sir how to solve equations of the type eg : find no of positive integral solutions of 7x+12y+4z=30 SOORAJ 
Re: Theory of Equations..  
Hey sir, I Want to know to solve this question \"If f(x) = x^2+2x5 and g(x) = 5x+30, then the roots of quadratic equation g[f(x) will be?\" ... Here what does g[f[x] mean? 
Re: Theory of Equations..  
Hey sir, I Want to know to solve this question \"If f(x) = x^2+2x5 and g(x) = 5x+30, then the roots of quadratic equation g[f(x) will be?\" ... Here what does g[f[x] mean? 