Question

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

Answer 1

Answer:

The sum of the roots of the equation $x^{2} + x = 2$ is -1

Step-by-step 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:

$x^{2}+\frac{b}{a} x+\frac{c}{a} =0$

and always the sum of roots will be given for this expression $x_{1} + x_{2} = \frac{-b}{a}$

Why this is true?

Because if we use the Quadratic Formula as follows:

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

$x_{1} + x_{2} = \frac{-2b+0}{2a}}$

$x_{1} + x_{2} = \frac{-b}{a}$

In the case of this equation:

$x_{1} + x_{2} = \frac{-1}{1} = -1$

Answer 2

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