### Video Transcript

Solve three 𝑥 squared plus two 𝑥
plus four is equal to zero. So if we just write out our
quadratic formula there, we can see that 𝑎 is three, 𝑏 is two, and 𝑐 is four. So plugging those values for 𝑎,
𝑏, and 𝑐 into the quadratic formula gives us 𝑥 is equal to negative two plus or
minus the square root of two squared minus four times three times four all over two
times three. Well, two squared is four, four
times three times four is forty-eight, so we’ve got four take away forty-eight in
that square root. And then two times three on the
denominator is six. So two possible solutions, negative
two plus the square root of negative forty-four all over six, or 𝑥 is equal to
negative two minus the square root of negative forty-four all over six. But if you try typing that into
your calculator, you’ll get a math error. The problem is this bit here,
square root of negative forty-four. There aren’t any real numbers that
you can multiply by themselves to give a negative answer. If you take a negative number and
multiply it by itself, you get a positive answer. And if you take a positive number
and you multiply it by itself, you get a positive answer. So there isn’t a real number that
you can multiply by itself that will give a negative answer.

Now if we have a look at the graph
of 𝑦 equals three 𝑥 squared plus two 𝑥 plus four, and then we put 𝑦 equal to
zero. We can see that, in fact, there
aren’t any 𝑥-values that are gonna generate a 𝑦-coordinate of zero. That curve doesn’t cut through the
𝑥-axis here. There are no 𝑥-values that
generate a 𝑦-coordinate of zero.

So this was a bit of a trick
question that broke the formula. We were asked to solve something
that doesn’t have any real solutions. So it seems like a bit of a trick
question, but really it’s just saying, you know, where does this quadratic curve cut
the 𝑥-axis on a curve that doesn’t cut the 𝑥-axis. So that’s what we found out. So when you’ve got a negative value
here for 𝑏 squared minus four 𝑎𝑐, you know you’ve got a curve that doesn’t cut
the 𝑥-axis.