SOLUTION: 22. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0? A. 0 and 3 B. –2 and 2 D. –3 and –1, 1, and 3

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 22. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0? A. 0 and 3 B. –2 and 2 D. –3 and –1, 1, and 3       Log On


   

Question 621223: 22. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0?
A. 0 and 3


B. –2 and 2


D. –3 and –1, 1, and 3
Answer by lwsshak3(11628) About Me  (Show Source):
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22. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0?
A. 0 and 3
B. –2 and 2
D. –3 and –1, 1, and 3
..
Using rational roots theorem
...0...|....3........-2.........0........1........-9.....
...1...|....3.........1.........1.........2........-7........
...2...|....3.........4.........8.........17.......25.... (2 is upper bound, all numbers>0)
==========================
...0...|....3........-2.........0.........1.........-9.....
.-1...|....3........-5.........5.......-4.........-5.....
.-2...|....3........-8........16......-31........53....(-2 is lower bound, numbers alternate in sign)
ans: B. -2 and 2