Consider the equation ax^{2 }+ bx + c = 0, with the 0 and let x'e x "be the real roots of this equation.

Soon:

Note the following relationships:

## Sum of roots (S)

## Root Product (P)

How we have:

We call these relationships **Girard Relations**. Check out some examples of applying these relationships.

Find the sum and root product of equation 10x

^{2}+ x - 2 = 0.**Solution**

In this equation we have: a = 10, b = 1 and c = -2.

The sum of the roots is equal to . The root product is equal to .

Like this: Like this:

Determine the value of

**k**in equation x^{2}+ (2k - 3) x + 2 = 0, so that the sum of its roots is equal to 7.**Solution**

In this equation we have: a = 1, b = 2k and c = 2.

S = x_{1}+ x_{2}= 7

Therefore, the value ofé -2.**k**