The discussion focuses on verifying the sum of the roots of a quadratic equation, specifically the relationship A + B = -b/a, where A and B are the roots of the equation ax² + bx + c = 0. The roots are derived using the quadratic formula: A = (-b + √(b² - 4ac)) / (2a) and B = (-b - √(b² - 4ac)) / (2a). Upon adding these two expressions, the radicals cancel out, leading to the simplified result of -b/a, confirming the theorem.
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There is a theorem for this, but let's do it logically. The two solutions, A and B of the quadratic areRTCNTC said:Let A and B be roots of the quadratic equation
ax^2 + bx + c = 0. Verify the statement.
A + B = -b/a
What are the steps to verify this statement?
topsquark said:There is a theorem for this, but let's do it logically. The two solutions, A and B of the quadratic are
[math]A = \frac{-b + \sqrt{b^2 - 4ac}}{2a}[/math] and [math]B = \frac{-b - \sqrt{b^2 - 4ac}}{2a}[/math]
Now add the two. (Hint: What happens to the radicals?)
-Dan