x^2 + mx + n = 0, x has to be -3, solve for m

Question

The answer is 6, but I don't understand the "why."

Answer 1

Jeremy,

 

This is a quadratic equation. By saying that the only solution to the equation is x = -3, this means that (x+3) must be a factor. Since -3 is the ONLY solution and the leading coefficient has a power of 2, this means that -3 is a double root. In other words (x+3) is a root of the function and has multiplicity of 2. This means the factored form of this equation is (x+3)^2 or (x+3)(x+3). When you expand this out you'll get x^2 + 6x + 9. As you can see from the expanded form, m = 6.