In details

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