To finish our problem,
we need to solve
the quadratic equation x squared
plus 2x minus 3 equals 0.
To do this, we'll use the
quadratic formula that
says the two roots,
r1 and r2, of 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
here our a is the coefficient
of x squared, which is 1,
b is the coefficient
of x, which is 2,
and c is the constant
coefficient negative 3.
So using the quadratic formula
in this particular example,
we have that our roots are
negative 2 plus or minus
the square root of 2 squared
minus 4 times 1 times negative
3 all over 2 times 1.
And we can simplify this
because 2 squared is 4,
negative 4 times 1 times
negative 3 is positive 12,
and 2 times 1 is 2.
So this becomes negative 2 plus
or minus the square root of 4
plus 12 all over 2.
And 4 plus 12 is 16,
whose square root is 4,
so we have negative 2
plus or minus 4 over 2.
Negative 2 plus 4 is 2, which
we have over 2, and negative 2
minus 4 is negative 6,
which we again have over 2.
And these reduce to
1 and negative 3.
So we've found
that the roots are
x equals 1 and x
equals negative 3.
