Consider the 2nd degree equation *ax ^{2} + bx + c = 0.* Dividing all terms by , we get:

How , we can write the equation this way.

x |

Examples:

Compose the 2nd degree equation whose roots are -2 and 7.

**Solution**:

The sum of the roots corresponds to:

S = x_{1}+ x_{2 }= -2 + 7 = 5

The root product corresponds to:

P = x_{1}. x_{2 }= ( -2) . 7 = -14

The 2nd degree equation is given by x^{2 }- Sx + P = 0, where S = 5 and P = -14.

So x^{2}- 5x - 14 = 0 is the searched equation.

Form the 2nd degree equation of rational coefficients, knowing that one of the roots is .

**Solution**:

If a 2nd degree equation of rational coefficients has a root , the other root will be .

Like this:

Soon,*x*the equation sought.^{2}- 2x - 2 = 0 is