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Question 1:
1 pts
$x = 3$ is a possible rational root of polynomial $$p(x)=x^5+3x^4-8.$$
Question 2:
1 pts
Which one of these is not possible real zero of $p(x) = 2x^3 + x^2 - 7x -1$:
1
$\frac{1}{2}$
2
$-\frac12$
Question 3:
2 pts
All possible rational roots of the polynomial $p(x)=2x^5-x^2+3$ are
$\pm 3 \pm1 \pm \frac32$
$\pm3 \pm1 \pm \frac{2}{3}$
$\pm\frac{1}{3}\pm1 \pm\frac{2}{3}$
$\pm\frac{1}{3} \pm1 \pm\frac{3}{2}$
Question 4:
2 pts
All possible rational roots of the polynomial $p(x)=4x^5-x^2+1$ are
$\pm1 \pm2 \pm4$
$\pm1 \pm4$
$\pm1 \pm2 \pm\frac{1}{4}$
$\pm1 \pm\frac{1}{2} \pm \frac{1}{4}$
Question 5:
2 pts
Usig a rational root test we can find all roots of the polynomial.
Question 6:
2 pts
$x= \sqrt{2}$ is a rational root of $p(x)=x^2-2$
Question 7:
2 pts
how many sign changes has polynomial $p(x)=x^3+x^2+x-1$.
$0$
$1$
$2$
$3$
Question 8:
2 pts
What is the sequence of pairs of successive signs for the polynomial $p(x)=x^3-x^2+x-3$
- + -
- + - +
+ + - -
+ - + -
Question 9:
3 pts
What is the maximum number of positive zeroes for the polynomial $$p(x) =-x^4-x^3+ x^2-1$$
$4$
$3$
$2$
$1$
Question 10:
3 pts
What is the number of negative zeroes for the polynomial $p(x) =x^6-x^5+2x^3-4x^2-1$
$4$
$3$
$2$
$1$
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