Question

Describe how you can determine the number of solutions when a quadratic equation is written in perfect square form.

Answer 1

A quadratic is an expression of the form ax²+bx+c.

If the quadratic is in the perfect square form, it could be factored to look something like this:

(x+a)² or (x-a)²

Both of the above forms have one solution, that is "-a" and "a" respectively.

So if your quadratic equation is of the form:

(x±a)² = b, where b > 0
You can solve for "x" by taking the square root of both sides and getting 2 solutions -- ±a±√b.

And if your quadratic equation is of the form:
(x±a)² = b, where b < 0
Then when you try taking the square root of both sides, you will have to take the square root of a negative number, which means you will not get a real solution.  Therefore, there will be zero solutions.

And finally if your quadratic equation is of the form:
(x±a)² = b, where b = 0
Then you will have one solution -- ±a.

Hope that helps!