SOLUTION: how do you create a quadratic equation with only one solution? For example -3?

Question 251041: how do you create a quadratic equation with only one solution? For example -3?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Given no other information than rational number solution, such as your example of -3, you can't create a unique quadratic equation. However, if you have either a real irrational solution or a complex solution, then you only have to realize that such solutions always come in conjugate pairs.

Let

and

be any rational numbers. Let

be a non-transcendental irrational number. Then if

is a root of the quadratic, then

is also a solution of the quadratic.

Let

and

be any real numbers. Let

be the imaginary number defined by

. Then if

is a root of the quadratic, then

is also a solution of the quadratic.

On the other hand, if you know another bit of information about the quadratic for which you have a single rational number solution, then you can derive an equation for the quadratic. For example, we know that the graph of a quadratic of the form

is a parabola symmetric to the vertical line that passes through its vertex. So if the vertex of the parabola is at

, and the quadratic has real number roots, then the two roots must be equidistant from the vertex, and therefore equidistant from the intersection of the parabola's axis and the