To finish our example,
we need to solve
the quadratic
equation 3x squared
plus 15x plus 12 equals 0.
To do this, we can use
the quadratic formula that
says that our two roots r1 and
r2 are given by the formula
negative b plus or minus
the square root of b
squared minus 4ac all over
2a, where our a, b, and c here
are 3, 15, and 12.
And plugging them in, we get
negative 15 plus or minus
the square root of 15
squared minus 4 times 3 times
12 all over 2 times 3.
Simplifying this, we get
that 15 squared is 225,
4 times 3 is 12,
times 12 again is 144.
And down bottom, we have
2 times 3, which is 6.
So we have negative 15 plus
or minus the square root
of 225 minus 144, all over 6.
And computing to 225
minus 144, we get 81,
and the square root of 81 is 9.
So we have negative 15
plus or minus 9 over 6.
Negative 15 plus 9 is negative
6, which we have over 6,
and negative 15
minus 9 is negative
24, which again we have over 6.
And these can both be reduced,
because negative 6 over 6
is negative 1, and negative
24 over 6 is negative 4.
So we can conclude that
the solutions to 3x
squared plus 15x plus 12 equals
0, our x equals negative 1
and negative 4.
