Question 384398
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:


<pre>


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


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(600,600,-5,5,-5,5,x^2 + 6*x + 9)}}}


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.