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The sum of the roots of the equation x 2 + x = 2 is:

User SofaKng
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hello :
x²+x - 2 =0
a=1 b=1 c = -2
The sum of the roots is : S = -b/a
S = - 1/1 = -1
User Yaniv Peretz
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Answer:

The sum of the roots of the equation
x^(2) + x = 2 is -1

Explanation:

You have two options to find the sum of the roots,

  1. The first option is to use the Quadratic Formula to find the two roots:


x_(1,2) = \frac{-b\±\sqrt{b^(2)-4ac}}{2a}


x^(2) + x - 2= where:

a = 1

b = 1

c = -2


x_(1) = \frac{-1-\sqrt{1^(2)-4*1*-2}}{2*1} = -2


x_(2) = \frac{-1+\sqrt{1^(2)-4*1*-2}}{2*1} = 1

The sum of the roots is -2 + 1 = -1

2. The second option is use the fact that a general quadratic equation is in the form of:


ax^(2)+bx+c=0

if you divided by
a you get:


x^(2)+(b)/(a) x+(c)/(a) =0

and always the sum of roots will be given for this expression
x_(1) + x_(2) = (-b)/(a)

Why this is true?

Because if we use the Quadratic Formula as follows:


x_(1) + x_(2) = \frac{-b+\sqrt{b^(2)-4ac}}{2*a} + \frac{-b-\sqrt{b^(2)-4ac}}{2a}


x_(1) + x_(2) = (-2b+0)/(2a)}


x_(1) + x_(2) = (-b)/(a)

In the case of this equation:


x_(1) + x_(2) = (-1)/(1) = -1

User BARJ
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