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Sum of roots

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2 Answers

If a(x-b)(x-c)=0,
then ax^2 - a(b+c)x + bc = 0.
 
The sum of the two roots is the opposite of the coefficient of the linear term divided by the leading coefficient.
 
Tom's 3rd line is 2x^2 - 7x -15 = 0.
 
We can immediately say the sum of the roots is 7/2.
2(x^2 -1) = 7x + 13
2x^2 - 2 = 7x +13
2x^2 - 7x -15 = 0
 
Factoring we get
(2x + 3) (x - 5) = 0
 
2X + 3 =0
 
2X = -3
X = -3/2
 
AND
 
x - 5 =0
x = 5