Question

Question from Axler's Algebra and Trigonometry

Answer 1

The question really does just want you to take the whole expression for x given by the quadratic formula and substitute it into ax² + bx + c, and verify that it all cancels down to 0. It might seem like a nightmare at first, but just be careful with your algebra and you should be fine. You also technically have to do it twice - once for each if the +- possibilities - but the work is 95% the same either way, so it shouldn't cause too much extra grief.

Answer 2

You'll need to do this in two steps.

Step 1: Start with ax^2 + bx + c. Everywhere you see an x, replace it with (-b-sqrt(b^2 - 4ac))/(2a). Show this works out to be zero.

Step 2: Start with ax^2 + bx + c again. Everywhere you see an x, replace it with (-b+sqrt(b^2 - 4ac))/(2a). Show this also works out to be zero.

Whoops. Just saw someone answered this four hours ago, haha