In details

Relations between coefficients and roots


Consider the equation ax2 + 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 10x2 + 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 x2 + (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 = x1 + x2 = 7

    Therefore, the value of k é -2.

Next: Composition of a 2nd Degree Equation