Solve three x squared plus x plus
one equals zero
well to begin solving this I might try to factor
and in factoring this I see that three x
squared
going to have to have three x and x
and multiply to a positive one
and add to a positive five x
my factors must be one and one
but if I multiply this back out I see that I
have three x squared
plus three x
plus x plus one
which is three x squared plus four x
plus one and four x is definitely not five
x
and so factoring does not look to be an
option because three x and x one and
one were my only choices
so factoring did not work
well if factoring doesn't work
I'm going to rely on the quadratic
formula
and reminder the quadratic formula is
opposite of b
plus or minus the square root of
b squared minus four
a c
all over two a
and this is when you have your quadratic
equation in terms of a x squared
plus b x plus c equals zero
and we do have that therefore we know
that a equals three
b equals five
and c equals one
listing these out will help me
basically plug those numbers in to solve
for my factors so the opposite of b or
negative b in this case is negative five
plus or minus the square root of
b squared, five squared, is twenty five
minus four
times a, which is three
times c which is one
all divided by two times a, which is three
simplifying this negative five can't
be simplified but
twenty five minus
four times three times one is twelve
twenty five minus twelve is
thirteen so I have the square root of thirteen
divided by two times three is six
and I cannot reduce negative
five plus or minus the square root of thirteen over
six
so that would be my final answer
