# For #x^2 - 6x +9 =0#, how many number of distinct solutions are there, and are they rational, irrational or non real complex numbers?

##### 2 Answers

There is one distinct solution for this equation which is

#### Explanation:

by factoring,

therefore,

There are

#### Explanation:

The quadratic equation is

Comparing this equation to the quadratic equation

Remember that the amount of solutions to a polynomial is equal to its degree. Here, since the degree is

The discriminant is

The discriminant tells us about the nature of the roots:

When:

As

To prove the above:

We can also simply obtain those roots by factorizing.