2-7-71
X
00:00
/
00:00
CC
We're going to take everything to one side.
Four X ^3 +5 X squared -7 X -2 greater than or equal to 0.
We're going to look at the graph and they've given US1 solution
of negative 1/4.
So if we use our synthetic division 4/5 negative seven -2
we always bring down the first number, multiply by the number
in the box, put it above the line in the next column, add.
Multiply by the number in the box, put it above the line in
the next column.
Add multiply by the number in the box, put it above the line
in the next column.
So this tells us X + 1/4 times four X ^2 + 4 X -8 needs to be
greater than or equal to 0.
Now we can actually pull a four out of this new polynomial.
If I pull a four out, I'm going to get a more simplified
polynomial that might be easier to see if it factors.
I also can multiply the four in through the first one, which is
nice because it gives me all integer coefficients.
That way X ^2 + X - 2 does indeed factor into X + 2 X -1.
So if we think about this polynomial, we know we have a
zero at negative 1/4, we know we have a zero at -2, and we know
we have a zero at 1:00.
We also know we have AY intercept at zero -2 because if
I put zero in for X in the original, these first three
terms all go away and we get left just the -2.
It's a third degree polynomial with a positive leading
coefficient.
So we're going to come out from Infinity.
We're going to go to this one.
This one had an odd multiplicity.
It's understood to be to a one.
So if the Y values are one side positive, the Y values on the
other side have to be negative.
We've got to go to the Y intercept and then up to the
next X intercept.
That one came from right here, and it's got a multiplicity of
one.
So if the Y values on one side are negative, the Y values on
the other side have to be positive.
Going to the last X intercept, it also has a multiplicity of
one, which is odd.
So if it's positive YS on one side, it's negative YS on the
other.
So our solution sets going to be -2 negative 1/4 and 1:00.