SOLUTION: draw an example of a quadratic equation that has two, one and no solutions.

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Question 727151: draw an example of a quadratic equation that has two, one and no solutions.
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Two solutions (x = -2 or x = 2)



Graph of above

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One solution (x = -5)



Graph of above

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No solutions



Graph of above
Answer by MathLover1(20849)   (Show Source): 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:
  1. 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 .
  2. 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 .
  3. 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

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