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  • 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 $p(x) =x^6-x^5+2x^3-4x^2-1$

    $4$

    $3$

    $2$

    $1$

Basics of polynomials

Polynomials Operations

Roots of polynomials

Factoring Polynomials

Graphing Polynomials

Rational exp. operations