In this example, we'll
solve the quadratic equation
x squared plus 1 equals 0.
Remember, the quadratic formula
says that the solutions to ax
squared plus bx plus c equals
0 are given by the formula
negative b plus or
minus the square root
of b squared minus
4ac all over 2a,
where a, b, and c are the
coefficients of our equation.
Here, a is 1, b
is 0, and c is 1.
So our formula becomes
negative 0 plus or minus
the square root of 0 squared
minus 4 times 1 times
1 all over 2 times 1.
Simplifying this, we have
that negative 0 is 0,
0 squared is 0 as well, 4 times
1 times 1 is 4, and 2 times 1
is 2.
So we have plus or minus
the square root of 0
minus 4 all over 2.
But 0 minus 4 is
negative 4, so we
have plus or minus the square
root of negative 4 over 2.
But the square root of negative
4 is not a real number.
So there are no real solutions.
So we can conclude that
there are no real solutions
to x squared plus 1 equals 0.
It's worth pointing
out the reason
there are no real solutions is
that negative 4 is less than 0.
So the square root
is not a real number.
And we have negative 4 is
less than 0 because negative 4
is b squared minus 4ac,
which is less than 0.
This is similar to what we
saw for repeated solutions.
It's also worth
pointing out that we
will learn more about the square
root of negative numbers soon.
