The Quadratic Formula is x equals negative
b plus or minus the square root of b squared
minus four "a", "c", all over two a.
We use this formula to solve quadratic equations
when they are written in standard form.
Which is ax squared plus bx plus c equals
zero.
Okay, let's do an example.
Solve two x squared minus five x plus six
equals zero.
When comparing it to the standard form you
should see that "a" is equal to two, "b" is
equal to negative five, and "c" is six.
Again writing the quadratic formula we have
x equals negative "b", plus or minus the square
root of "b" squared minus four "a", "c".
All over two "a".
Notice how I put parenthesis where each letter
will go and now we can fill each in.
"A" goes here and here.
"B", which is negative five goes here and
here, and "C" which is six goes here.
Simplifying this we get negative, negative
five is positive five.
Plus or minus the square root of negative
five squared, which becomes twenty-five minus
four times two times six is forty-eight.
All over two times two, which is four.
Twenty-five minus forty-eight gives us negative
twenty-three.
And this can also be written as five over
four plus or minus square root of negative
twenty-three over four.
The square root of a negative number is imaginary,
so we will write our final answer as five
fourths plus or minus square root of twenty-three
over four i.
If the square root of twenty-three could have
been simplified, we would have done that also,
but since it cannot this is our final answer.
Since the answer contains i what we have are
two complex solutions.
One plus and one minus.
This means that the graph of this equation
will have no x-intercepts.
