College Algebra, 2013a

3.3 Real Zeros of Polynomials 283
3.3.4 Answers
1. For f(x) =x 3 − 2x 2 − 5x +6
ˆ All of the real zeros lie in the interval [−7, 7]
ˆ Possible rational zeros are ±1, ±2, ±3, ±6
ˆ There are 2 or 0 positive real zeros; there is 1 negative real zero
2. For f(x) =x 4 +2x 3 − 12x 2 − 40x − 32
ˆ All of the real zeros lie in the interval [−41, 41]
ˆ Possible rational zeros are ±1, ±2, ±4, ±8, ±16, ±32
ˆ There is 1 positive real zero; there are 3 or 1 negative real zeros
3. For f(x) =x 4 − 9x 2 − 4x +12
ˆ All of the real zeros lie in the interval [−13, 13]
ˆ Possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±12
ˆ There are 2 or 0 positive real zeros; there are 2 or 0 negative real zeros
4. For f(x) =x 3 +4x 2 − 11x +6
ˆ All of the real zeros lie in the interval [−12, 12]
ˆ Possible rational zeros are ±1, ±2, ±3, ±6
ˆ There are 2 or 0 positive real zeros; there is 1 negative real zero
5. For f(x) =x 3 − 7x 2 + x − 7
ˆ All of the real zeros lie in the interval [−8, 8]
ˆ Possible rational zeros are ±1, ±7
ˆ There are 3 or 1 positive real zeros; there are no negative real zeros
6. For f(x) =−2x 3 +19x 2 − 49x +20
ˆ All of the real zeros lie in the interval [ − 51
2 , 51 ]
2
ˆ Possible rational zeros are ± 1 2 , ±1, ±2, ± 5 2
, ±4, ±5, ±10, ±20
ˆ There are 3 or 1 positive real zeros; there are no negative real zeros
7. For f(x) =−17x 3 +5x 2 +34x − 10
ˆ All of the real zeros lie in the interval [−3, 3]
ˆ Possible rational zeros are ± 1
17 , ± 2
17 , ± 5
17 , ± 10
17
, ±1, ±2, ±5, ±10
ˆ There are 2 or 0 positive real zeros; there is 1 negative real zero