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March 19th, 2014, 07:09 PM  #1 
Senior Member Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus  Finding the equation when givien two roots
Why is a(x  r?)(x  r?) the general form of finding a quadratic equation when given two roots? Why is there an "a" constant?

March 19th, 2014, 07:20 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,937 Thanks: 2265 Math Focus: Mainly analysis and algebra  Re: Finding the equation when givien two roots
Because a general quadratic is and which has a coefficient of 1 for the term in .

March 19th, 2014, 07:24 PM  #3 
Senior Member Joined: Mar 2014 Posts: 112 Thanks: 8 
That's because let 0 = ax² + bx + c where a ? 0. 0 = a(x  r_1)(x  r_2) = ax²  a(r_1 + r_2)x + ar_1r_2 where b = a(r_1 + r_2) and c = ar_1r_2. Of course we could always divide both sides of the equation by a and get 0 = x² + bx/a + c/a or 0 = (x  r_1)(x  r_2). 

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