Download PRECALCULUS HONORS TEST REVIEW 2.5 Find all the zeros of

PRECALCULUS HONORS TEST REVIEW
2.5
Find all the zeros of the function.
1.
f (x) = 3x(x − 2)2
2.
f (x) = x 3 + 6x
3.
f (x) = (x − 8)(x − 5)2 (x − 3 + i)(x − 3 − i)
Use the Rational Zero Test to list all possible rational zeros of f.
4.
f (x) = −4 x 3 + 8x 2 − 3x + 15
Find all rational zeros of the function.
5.
f (x) = x 3 − 2x 2 − 21x − 18
6.
f (x) = 25x 4 + 25x 3 − 154 x 2 − 4 x + 24
Find a polynomial function with real coefficients that has the given zeros. (There are many correct
answers.)
7.
2
, 4, i 3
3
Use the given zero to find all the zeros of the function.
8.
f (x) = x 3 − 4 x 2 + x − 4
9.
f (x) = 2x 4 − 3x 3 − 13x 2 + 37x − 15
zero : i
zero : 2 + i
Find all the zeros of the functions and write the polynomial as a product of linear factors.
10. f (x) = x 4 + 8x 3 + 8x 2 − 72x − 153
11. f ( x) = 3 x 3 − 20 x 2 + 7 x + 30
Use Descartes’s Rule of Signs to determine the possible numbers of positive and negative zeros of the
function.
12. g(x) = 5x 3 + 3x 2 − 6x + 9
Use synthetic division to verify the upper and lower bounds of the real zeros of f.
f (x) = 4 x 3 − 3x 2 + 4 x − 3
13. (a) Upper:
(b) Lower:
x =1
x=−
1
4