If 2 x 2 − 4 x = 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 , find the sum of the roots of the equation.
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By Vieta's formula .
Sum of roots =
a
−
b
∴
2
4
=
2
By Vieta, the sum of the roots is − a b , so the answer is − 2 − 4 = 2
In a quadratic equation, a x 2 + b x + c = 0 , the sum of the roots is a − b . Substitute:
x 1 + x 2 = 2 − ( − 4 ) = 2
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To satisfy my own interests, ( x − 1 ) 2 = 5 ( 1 0 1 4 ) , or simply x = 1 ± 1 0 7 5 , whose sum is 2.