# Composition of an equation of the 2nd degree, known as the roots

Consider the 2nd degree equation ax2 + bx + c = 0. Dividing all terms by , we get:

How , we can write the equation this way.

 x2 - Sx + P = 0

Examples:

• Compose the 2nd degree equation whose roots are -2 and 7.
Solution:
The sum of the roots corresponds to:
S = x1 + x2 = -2 + 7 = 5
The root product corresponds to:
P = x1 . x2 = ( -2) . 7 = -14
The 2nd degree equation is given by x2 - Sx + P = 0, where S = 5 and P = -14.
So x2 - 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, x2 - 2x - 2 = 0 is the equation sought.

Next: Factored Form