which of these rational numbers does rational roots therorem say cant be a solution for 14x^7+13x^5-19x^4+7x^2-6x-21=0
a.3/2
b. -1
c. 2/7
d. -1/2
2. which are upper and lower bounds for the real roots of 3x^4-2x^3+x-9=0
a. 0 and 3
b. -2 and -1, 1, and 2
c. -3 and -1, 1, and 3
d. -2 and 2
3. which of the folllowing is the conclusion you can draw using descartes rule of signs applied to 2x^4-6x^3+x^2+7x-4
a. there is 1 neg real root. there are either 0 or 2 complex roots
b. there are 3 neg roots. there are 0 or 2 complex roots
c. there is 1 neg real root. no info is avail about the # of complex roots
d. 3 neg real roots. no info is avail about the # of complex roots
if someone can help me out I would really apprecite it
a.3/2
b. -1
c. 2/7
d. -1/2
2. which are upper and lower bounds for the real roots of 3x^4-2x^3+x-9=0
a. 0 and 3
b. -2 and -1, 1, and 2
c. -3 and -1, 1, and 3
d. -2 and 2
3. which of the folllowing is the conclusion you can draw using descartes rule of signs applied to 2x^4-6x^3+x^2+7x-4
a. there is 1 neg real root. there are either 0 or 2 complex roots
b. there are 3 neg roots. there are 0 or 2 complex roots
c. there is 1 neg real root. no info is avail about the # of complex roots
d. 3 neg real roots. no info is avail about the # of complex roots
if someone can help me out I would really apprecite it
-
Number 1:
The answer is C since 21 does not have 2 as a factor.
Number 2:
I am not sure about this. It might be either a or c.
Number 3:
f(x) = 2x^4 - 6x^3 + x^2 + 7x - 4
If we count the number of sign changes from left to right, we get 3 sign changes. That means there are either 1 or 3 positive real roots
f(-x) = 2x^4 + 6x^3 + x^2 - 7x - 4
Counting the number of sign changes from left to right we get 1 sign change, which means there is one negative real root.
The answer is A
The answer is C since 21 does not have 2 as a factor.
Number 2:
I am not sure about this. It might be either a or c.
Number 3:
f(x) = 2x^4 - 6x^3 + x^2 + 7x - 4
If we count the number of sign changes from left to right, we get 3 sign changes. That means there are either 1 or 3 positive real roots
f(-x) = 2x^4 + 6x^3 + x^2 - 7x - 4
Counting the number of sign changes from left to right we get 1 sign change, which means there is one negative real root.
The answer is A