Consider the equation ax2 + bx + c = 0, with the 0 and let x'e x "be the real roots of this equation.
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.
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 .
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Determine the value of k in equation x2 + (2k - 3) x + 2 = 0, so that the sum of its roots is equal to 7.
In this equation we have: a = 1, b = 2k and c = 2.
S = x1 + x2 = 7
Therefore, the value of k é -2.