16.2d Quadratic Formula-Missing Terms.
If we have a term missing from our quadratic, we want to use zero in the quadratic formula.
Let's see how that works.
So in our first example here, I notice that
I have an a, and I have my c.
What I am missing is my b, so we want to use b equals zero.
So when I throw this in my Quadratic Formula my x equals our b which is, zero plus or minus
the square root of our b squared, which is
zero
minus four times our a, times our c, all over two times our a.
So we're going to get x equal to plus or minus the square root of a negative four times our
three times our fifty-four, giving us, a negative 648 - all over six.
So let's see about simplifying our 648.
We have x equal to plus or minus square root of, let's see, okay, so 648 is when we do
some factoring here basically comes down to it's four times nine, times nine, times 2, 'kay, and we
still have that negative. So we should have done this: that means we're going to have
two, and a nine come out which, is going to give us, eighteen, we have the negative which is going
to give us i; and then we're going to have
the two still inside, all over six.
Eighteen and six have a common factor of six,
so we're going to get x equal to plus or mins 3i square root two.
Alright, let's look at our second example.
Well we need to get everything on one side. So we have 5x squared minus 2x equal to zero.
So this is, our a and we have b, and then
c is going to be equal to zero because, there is none.
So now we get, x equal to the opposite of
our b plus or minus the square root of b squared,
minus four, times our a, times our c, all over two times our a.
So what we get then is x equal two plus or minus, the square root of four because, all this last part disappear.
So we have x equal to two plus or minus two all over ten. So two minus two is zero.
So we are going to get x is equal to zero
for one.
And then two plus two is four, and that four over ten is going to give us two-fifths and we're done.
