Question

How many different ways can you solve a quadratic equation? List them.

Answer 1

1) Quadratic Formula is like the swiss army knife when it comes to this. Never fails, but not convenient sometimes.

2) Consider the polynomial:
x^2 + Ax + B = 0
Note that the leading coefficient is 1. Then you find two terms, say x1 and x2, whose product is B and sum is A.
Then: x^2 + Ax + B = (x-x1)(x-x2)
Sometimes, you just need a good hunting knife.

3) Consider the polynomial Ax^2 - k^2, such that A and k are real numbers.
(A^2)(x^2) - k^2 =
(Ax+k)(Ax-k)

4) Splitting the middle term.

5) Rational Root Theorem and Synthetic Division

6) Graph and approximate solutions.