You can put this solution on YOUR website! How to determine the number of solutions.
Let's look at the quadratic formula:
The key is the expression in the square root: .
In general there are three cases:
is positive.
The square root of a positive number is also some positive number.
So in the numerator of the quadratic formula we will get two values:
( + the square root) and ( - the square root).
So when we get .
is zero.
The square root of zero is zero. So in the numerator we get () and ().
But both of these are equal to !
So when we only get .
is negative. What is the square root of a negative number? What can we square and get a negative number as an answer? Answer: .
You cannot square any Real number and get a negative. So, when there are .
example:
1. ... which is ..=> ; so, we have
2.
... which is ..=> ; so, we have
3.
... which is ..=> ; so, we have
(