In this example,
we'll find solutions
to the quadratic equation
3x squared plus x equals 0.
We will do this using the
quadratic formula that
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.
And using our a, b, and
c from this equation,
we have that a is 3, our
coefficient of x squared,
b is 1, our coefficient of
x, and c is 0, our constant.
So our two solutions
are negative 1
plus or minus the square root of
1 squared minus 4 times 3 times
0, all over 2 times 3.
Simplifying this, we
get that 1 squared is 1,
and minus 4 times 3
times 0 is minus 0.
So in the square
root, we just have 1.
And down bottom, 2 times 3 is 6.
So we have negative
1 plus or minus
the square root of 1 over 6.
But the square root of 1 is 1.
So we have negative 1
plus or minus 1 over 6.
Negative 1 plus 1 is 0,
and negative 1 minus 1
is negative 2.
And both of these are over
6, which we can reduce,
because 0 over 6 is 0
and negative 2 over 6
is negative 1/3.
So we can conclude that the
solutions to 3x squared plus x
equals 0 are x equals
0 or negative 1/3.
