In this example, we'll
solve the quadratic equation
2x squared minus 3 equals 0.
We will do it using the
quadratic formula, which
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.
In this example, our a is 2,
the coefficient of x squared.
B is 0, since we have 0x.
And c is negative
3, our constant.
Plugging these in, we get
that our roots are negative 0
plus or minus the square root of
0 squared minus 4 times 2 times
negative 3, all over 2 times 2.
But 0 squared is 0, and negative
4 times 2 is 8 times negative
3 is positive 24.
So under the square
root, we have 0 plus 24.
And down bottom, we have
2 times 2, which is 4.
0 plus 24 is just 24
under our square root.
So we get our roots are plus
or minus the square root
of 24 over 4.
So we can conclude that the
solutions to 2x squared minus 3
equals 0 are x equals plus or
minus the square root of 24
over 4.
Even though this is messy, we
have found the values of x.
And we can make this
a little bit nicer.
If we notice that
the square root of 24
can be split up as the
square root of 4 times 6,
which is the square root of
4 times the square root of 6.
And the square root of 4 is 2.
So this is 2 times
the square root of 6.
So we get that our solutions
are plus or minus 2
over the square
root of 6, which can
be reduced to plus or minus
the square root of 6 over 2.
So we can conclude that the
solutions to 2x squared minus 3
equals 0 are x equals plus
or minus the square root of 6
over 2.
It's worth noting that even
though our solutions here
are messy, we were
still able to find them.
This is a good thing.
This means that even if we
have complicated equations
with hard to find
solutions, we can still
get them using the
quadratic equation.
