SOLUTION: How can you have one solution in something that is quadratic?

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Question 384398: How can you have one solution in something that is quadratic?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
When b^2 - 4ac is equal to 0, you will have 1 solution.

The standard form of the quadratic equation is:

ax^2 + bx + c = 0

a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term.

To find the roots of this equation, you can use the quadratic formula.

the quadratic formula is: 



x = -b +/- sqrt(b^2-4ac)
    --------------------
             2a


If b^2 - 4ac is equal to 0, then you have +/- 0 in the numerator and there is only one solution to the problem.

We can construct an example to show you what I mean.

To construct this example, let's pick a b term at random.

Let's say b is equal to 6.

That makes b^2 = 36

Divide 36 by 4 to get 9.

We need to get a * c to be equal to 9.

a * c will be equal to 9 when a = 1 and c = 9

We have:

a = 1
b = 6
c = 9

b^2 - 4ac becomes 36 - (4*1*9) which becomes 36 - 36 which becomes 0.

Our quadratic equation should have one solution only.

The standard form of the quadratic equation is ax^2 + bx + c = 0

Since a = 1, b = 6 and c = 9, this equation becomes:

x^2 + 6x + 9 = 0

We will now graph this equation as shown below:

graph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E2+%2B+6%2Ax+%2B+9%29

You can see from the graph that the graph of the quadratic equation touches the x-axis at the point x = -3 and only at that point.