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• Polynomials
• Roots of Polynomials
• Rational roots and Descartes rule

Rational roots and Descartes rule

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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 $p(x) =x^6-x^5+2x^3-4x^2-1$
 $4$ $3$ $2$ $1$