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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: 7,268 Thanks: 2434 Math Focus: Mainly analysis and algebra Re: Finding the equation when givien two roots Because a general quadratic is $ax^2 + bx + c$ and $(x-r_1)(x-r_2)= x^2 - (r_1+r_2)x + r_1r_2$ which has a coefficient of 1 for the term in $x^2$.
 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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