Please explain in the simplest terms how to solve the following: (in the description)

Question

If x₁,x₂ are the roots of the equation x² + 5x - 3 = 0, determine the value of x₁ + x_2.

Answer 1

Given the equation x² + 5x - 3 = 0, the simplest way we can find its roots is by using the Quadratic formula which always works if you are trying to find the zeros given a quadratic equation in standard form (ax² + bx + c) which this equation is. Usually it is easier to factor and then use the zero product rule to find the roots but this equation cannot be factored nicely over integers or rational numbers since nothing is a product of 3 and adds up to 5 which is why we use the quadratic formula:

Quadratic formula: x = (-b ± √b²-4ac) / (2a)

From the equation, we can state that a = 1, b = 5, and c = -3. So, lets plug those into the formula:

x = [-5 ± (√5²-4(1)(-3))] / [2(1)]

= [-5 ± (√25+12)] / 2

= [-5 ± √37] / 2

So, the roots are:

x = (-5 + √37) / 2,

x = (-5 - √37) / 2

Adding the roots gives us:

[(-5 + √37) / 2] + [(-5 - √37) / 2] = -5

So, adding the roots gives us -5 which is our answer.

Answer 2

,If x₁,x₂ are the roots of the equation x² + 5x - 3 = 0, determine the value of x₁ + x_2.

The two values of the quadratic equation are given as

X1 = ⌈-5+√(25 +4*3)⌉/2 = ⌈-5+√37⌉/2

and

X2 =⌈-5 - √(25 +4*3)⌉/2 = ⌈-5-√37⌉/2

Gives X1 +X2 = -10/2 = -5