The Sum and Product of Roots of a Quadratic Equation
Introduction
Let s, t be the roots of the equation a*x^2 + b*x + c = 0.
Let:
s = (-b + √(b^2 - 4*a*c)) / (2 * a)
t = (-b - √(b^2 - 4*a*c)) / (2 * a)
Then
s + t = -b / a
s * t = c / a
We see this topic a lot in algebra, let's see how these properties are derived. Fairly simple.
Sum of the Roots
s + t
= (-b + √(b^2 - 4*a*c)) / (2 * a) + (-b - √(b^2 - 4*a*c)) / (2 * a)
= (-2 * b) / (2 * a)
= -b / a
Product of the Roots
s * t
= (-b + √(b^2 - 4*a*c)) / (2 * a) * (-b - √(b^2 - 4*a*c)) / (2 * a)
= (b^2 + b * √(b^2 - 4*a*c) - b * √(b^2 - 4*a*c) - (b^2 - 4*a*c)) / (4*a^2)
= (b^2 - b^2 + 4*a*c) / (4*a^2)
= (4*a*c) / (4*a^2)
Eddie
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