Question

Part 1: Which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring and why?

1. −b
2. b2 − 4ac
3. 2a
Part 2: Create your own quadratic equation. Using complete sentences, and your answer from part 1, determine whether your equation can be solved by factoring.

Answer 1

If b^2 - 4ac is a perfect square, then the roots are rational, and the quadratic can be factored.

Answer 2

b^2 - 4ac ==> this is the discriminant
note: for real numbers a, b and c,,
*if b^2 - 4ac < 0 : 2 imaginary roots
*if b^2 - 4ac = 0 : 1 real and distinct root
*if b^2 - 4ac > 0 : 2 real and distinct roots