Question 768470: how do i find all the real zeros of 2x^3+6x^2+5x+3? i found all the possible real zeros, but when i tried to solve for the real ones, i couldnt find any. the PRZ=1, -1, 3, -3, .5, -.5, 3/2, -3/2
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! how do i find all the real zeros of 2x^3+6x^2+5x+3? i found all the possible real zeros, but when i tried to solve for the real ones, i couldnt find any. the PRZ=1, -1, 3, -3, .5, -.5, 3/2, -3/2
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Real Number solution:::
I graphed the cubic and found a Real Number solution at x = -2.1654
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Cheers,
Stan H.
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
As you see from the other tutor's graph, there are NO rational zeros.
The zero he gave is IRRATIONAL,
which means that the decimal x = -2.1654 is only an approximation
because the decimal goes on forever with no particular pattern.
It is x = -2.1653730430624... to 13 decimal places, but the decimals
never stop or form any particular pattern.
"PRZ" means "possible RATIONAL zeros" not "possible REAL zeros".
The "R" stands for "RATIONAL", not "REAL".
So the list 1, -1, 3, -3, 1/2, --1/2, 3/2, -3/2
is only the list of possible RATIONAL zeros.
Actually the word "POSSIBLE" is a misnomer. Because it
may be that there are NO rational zeros, as in your
example.
So the list 1, -1, 3, -3, 1/2, --1/2, 3/2, -3/2
is only a list of MAYBES for rational zeros, as there
may be NO rational zeros.
Now if there were any rational zeros, they will be included in
that list. But they are always only 'maybes'!
So PRZ should be MRZ (Maybe's for RATIONAL zeros) J
Edwin
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