MHB How Can You Verify the Sum of Roots in a Quadratic Equation?

[mathdad]

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]

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?

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

 

[mathdad]

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

The radicals disappear. We are then left with (-2b)/(2a).
Of course, (-2b)/(2a) simplifies to -b/a.