Question

What is the mathmatic reason for some quadratic equations have only one answer, rather than the usual two? I suppose that sometimes it concerns limitations involving zero: can't divide by it, etc. Thanks.

Answer 1

below

Explanation:

According to the Fundamental Theorem of Algebra a quadratic has 2 solutions. When we find only one solution we write it as , say, ,3 multiplicity 2'. In other words 2 solutions which are duplicates.

For example x^2 + 4x + 4 = 0 factors to:

(x + 2)(x + 2) = 0

so x = -2 multiplicity 2.

The graph of this function will be the usual U shaped curve where the vertex just touches the x axis at the point (-2, 0).