In this example, we'll
find the solutions
to the quadratic
equation 6x squared
plus x minus 2 equals 0.
Remember that solutions
to an equation where
one side is 0 we call roots.
And we found in the
quadratic formula
that our two roots r1
and r2 of the equation 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
the numbers a, b, and c
in the formula come from
a, b and c in our equation.
In this example, our a is 6,
the coefficient of x squared,
b is 1, the coefficient
of x, and c is negative 2,
our constant.
So plugging these
into our formula,
we get that our roots are
negative 1 plus or minus
the square root of 1
squared minus 4 times 6
times negative 2 all over 2
times 6, which we can simplify.
Negative 1 is just negative 1.
1 squared is 1.
And negative 4 times 6
is 24, times negative 2
is positive 48.
So inside the square
root, we have 1 plus 48.
And down bottom, we have
2 times 6, which is 12.
So we have that our
roots are negative 1
plus or minus the square
root of 1 plus 48 over 12.
And 1 plus 48 is 49, and
the square root of 49 is 7.
So we get that our roots
are negative 1 plus or minus
7 over 12.
Negative 1 plus 7 is 6,
which we have over 12.
And negative 1 minus
7 is negative 8,
which, again, is over 12.
These two fractions
we can simplify.
6 over 12 is 1/2, and negative
8 over 12 is negative 2/3.
So we can conclude that
the solutions to 6x
squared plus x
minus 2 equals 0 are
x equals 1/2 and negative 2/3.
