Question 1089810: 5.
Use the rational zeros theorem to list the potential rational zeros of the polynomial function. Do not attempt to find the zeros.
f (x) = 2x^11−x^9+ 3x^8 + 28
Find the potential Rational zeros.
A.
−1, 1, −2, 2, −4, 4, −7, 7, −14, 14, −28, 28, −1/2, 1/2, −7/2, 7/2
B.
−1, 1, −2, 2, −4, 4, −7, 7, −28, 28, −1/2, 1/2, −1/28, 1/28
C.
−1, 1, −2, 2, −4, 4, −7, 7, −28, 28, −1/2, 1/2, −7/2, 7/2, −1/28, 1/28
D.
−1, 1, −2, 2, −4, 4, −7, 7, −14, 14, −28, 28, −1/2, 1/2, −1/28, 1/28
Choose A, B, C, OR D. (SHOW WORK)
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52847)   (Show Source):
You can put this solution on YOUR website! .
Use the rational zeros theorem to list the potential rational zeros of the polynomial function. Do not attempt to find the zeros.
f (x) = 2x^11−x^9+ 3x^8 + 28
Find the potential Rational zeros.
A.
−1, 1, −2, 2, −4, 4, −7, 7, −14, 14, −28, 28, −1/2, 1/2, −7/2, 7/2 <<<---=== This answer is correct.
B.
−1, 1, −2, 2, −4, 4, −7, 7, −28, 28, −1/2, 1/2, −1/28, 1/28
C.
−1, 1, −2, 2, −4, 4, −7, 7, −28, 28, −1/2, 1/2, −7/2, 7/2, −1/28, 1/28
D.
−1, 1, −2, 2, −4, 4, −7, 7, −14, 14, −28, 28, −1/2, 1/2, −1/28, 1/28
Choose A, B, C, OR D. (SHOW WORK)
On rational root theorem see this Wikipedia article
https://en.wikipedia.org/wiki/Rational_root_theorem
The potential roots are all integer divisors of the constant term 28, AND all fractions of dividing these divisors by 2.
Answer by math_helper(2461)  (Show Source):
You can put this solution on YOUR website! All the potential zeros have the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient. Since the constant term is 28, p can take on +/- { 1,2,4,7,14,28}. Since the leading coefficient is 2, q can take on values +/-{1,2}
—
Answer A is the only one that has all p/q that fit these constraints.
[ It is easy to eliminate the other choices because they each have +/- 1/28 ].
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