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March 19th, 2014, 07:09 PM   #1
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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?
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March 19th, 2014, 07:20 PM   #2
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Re: Finding the equation when givien two roots

Because a general quadratic is and which has a coefficient of 1 for the term in .
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March 19th, 2014, 07:24 PM   #3
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That's because let 0 = ax + bx + c where a ? 0.
0 = a(x - r_1)(x - r_2) = ax - 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 = x + bx/a + c/a or 0 = (x - r_1)(x - r_2).
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