What is an example of using the quadratic formula?
Suppose that you have a function represented by
We can use the quadratic formula to find the zeroes of this function, by setting
Technically we can also find complex roots for it, but typically one will be asked to work only with real roots. The quadratic formula is represented as:
#(-B +- sqrt(B^2-4AC))/(2A) = x#
... where x represents the x-coordinate of the zero.
As an example, consider the function
#A = 1, B = -13, C = 12.#
Then for the quadratic formula we would have:
# x = (13 +- sqrt ((-13)^2 - 4(1)(12)))/(2(1))#=
#(13 +- sqrt (169 - 48))/2 = (13+-11)/2#
Thus, our roots are
For an example with complex roots, we have the function
Then by the quadratic equation,
#x = (0 +- sqrt (0^2 - 4(1)(1)))/(2(1)) = +-sqrt(-4)/2 = +-i#
In the graph for this function on the real coordinate plane, we will see no zeroes, but the function will have these two imaginary roots.