Question

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

Answer 1

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

Answer 2

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`