(male narrator)
In this video,
we will look at using
the quadratic formula
when one or more of the terms
is missing.
If a term is missing,
we will simply use 0
as we plug in values
for the quadratic formula.
For example,
in this problem,
you may notice
that there is no x term.
This means
we can think
about there being 0x
in the middle.
So 7 would be our a;
and for b, we'll use that 0;
while -49 is our c.
Plugging these values
into the quadratic formula,
we have x equals
the opposite of b, or 0;
plus or minus the square root
of b, or 0 squared;
minus 4a, which is 7;
c, which is -49;
all over 2a, which is 7.
We can ignore the 0s,
as they won't have any effect
on our problem,
and we get x is equal
to plus or minus the square root
of 4 times 7;
times 49, is 1,372;
over 2 times 7, which is 14.
To simplify that radical,
we'll need to find out
what goes into 1,372;
which is divisible by 2,
686 times;
which is divisible by 2,
343 times;
which is divisible by 7,
49 times;
which is divisible by 7,
7 times; and 7, once.
So now, we have
x is equal
to plus or minus
the square root of 2 squared,
times 7 cubed,
over 14.
We can take
the square root of 2 squared,
dividing the exponent
by the index,
and the 7 cubed,
with one 7 remaining behind.
We now have x is equal
to plus or minus;
2 times 7 is 14;
square root of 7;
over 14;
14s divide out;
and for our final answer,
x is equal to plus or minus
the square root of 7.
Let's try
one more problem
where we have to use 0
for a missing term
and simplify what remains
in the quadratic formula.
Again, you notice
the x term is missing,
so we'll think about this
as having 0x:
a is 3, b is 0,
and c is 54.
Plugging these values
in the quadratic formula,
we get x is equal
to the opposite of b, or 0;
plus or minus the square root
of b, or 0 squared;
minus 4a, which is 3;
times c, which is 54;
all over 2a,
which is 3.
The 0s can be ignored as we
multiply what's left together:
x is equal to plus or minus
the square root of -4 times 3;
times 54, is -648;
all over 2 times 3, which is 6.
We can then factor
what's left
to see if we can simplify
that radical.
If it's negative,
we'll use -1 as a factor
and then see how 648
can be factored out.
It's divisible by 4...or 2,
sorry...2, 324 times;
which is divisible by 2,
162 times;
which is divisible by 2,
81 times;
which is divisible by 3,
27 times;
3, 9 times; 3, 3 times;
and 3, once.
This means
we have factors:
2 cubed, times 3 to the 4th,
all over 6.
We can pull a 2 cubed out
with one 2 remaining;
3 to the 4th will come out
as 3 squared, or 9;
and then -1
will come out as an i.
This means we have x
is equal to plus or minus 18i,
times the square root of 2,
over 6.
We can then simplify
the 18 over 6 to get 3,
and x is equal
to plus or minus 3i,
times the square root of 2,
and this becomes
our final solution.
As you can see,
if a term is missing,
we simply use 0
for that term
and can use the quadratic
formula like always--
simplifying
the entire expression.
