What are all the possible rational zeros for #f(x)=x^3+3x^2+x-2# and how do you find all zeros?
2 Answers
All the zeroes of
only rational zero is
Explanation:
We observe that the sum of the co-effs. of
Also, the sum of the co-effs. of odd-powered terms is 2, and that
of even-powered 1, Since, these are not equal, so,
not a factor.
Now,
Hence, the possible linear factors
We have already verified that
For
Now,
For the Quadratic
Thus, all the zeroes of
only rational zero is
Enjoy Maths.!
All the possible rational zeros for f(x) are
all zeros are -2 (rational) and
Explanation:
All the possible rational zeros for f(x) are the factors of the known term 2:
You would apply the remainder rule to find the first zero:
and you conclude that 1 isn't a zero for f(x);
and you conclude that -1 isn't a zero for f(x);
and you conclude that 2 isn't a zero for f(x);
then -2 is a zero for f(x)
Then you would divide f(x) by (x+2) and get the polynomial:
that, solved by the quadratic formula, will give the not rational zeros: