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  • Polynomials
  • Roots of Polynomials
  • Properties of polynomial roots

Properties of polynomial roots

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  • Question 1:
    1 pts
    		$x=3$ is a root of polynomial $p(x) = x^2-x-6$.
  • Question 2:
    1 pts
    		$x=-1$ is a root of polynomial $p(x) = x^3-x+2x+3$
  • Question 3:
    1 pts
    		The graph of the polynomial $p(x)$ is given at the right. How many positive roots does $p(x)$ has?
    0
    1
    2
    3
  • Question 4:
    2 pts
    		How many distinct roots does polynomial $p(x) = (x+1)^2$ has

    $0$

    $1$

    $2$

    $3$

  • Question 5:
    2 pts
    		One zero of $p(x) = x^2+2x+2$ is $1+i$. Which of the following is another zero?

    $i$

    $i-1$

    $1-i$

    $-i$

  • Question 6:
    2 pts
    		One zero of $p(x) = x^3- 3x^2+ x + 5$ is $2 - i$. Which of the following is another zero?

    $2$

    $2+i$

    $i-2$

    $i$

  • Question 7:
    2 pts
    		The equation of polynomial whose graph is shown in the figure is:
    $p(x)=(x+2)(x+1)$
    $p(x)=(x-2)(x-1)$
    $p(x)=(x+2)(x-1)$
  • Question 8:
    2 pts
    		Polynomial $p(x)$ has roots $x=1$ and $x=2$. $$p(x)=$$
    $x^2-2x+1$
    $x^2+x-4$
    $x^2-3x+2$
    none of these
  • Question 9:
    3 pts
    		Polynomial $p(x)$ has roots $x=1$ , $x=5$ and $x=0$. $$p(x) = $$
    $x^3-5x^2+6x$
    $x^3-6x^2+5x$
    $x^3-x^2$
    none of these
  • Question 10:
    2 pts
    		Multiplicity of root $x=1$ in polynomial $p(x)=(x+1)^2$ is 2.
  • Question 11:
    2 pts
    		multiplicity of root $x=1$ in polynomial $p(x)=3(x-1)^2(x+1)^3$ is 3.
  • Question 12:
    2 pts
    		Polynomial $p(x)$, with leading coefficient 6, has a root of multiplicity 7 at $x=0$. The equation of polynomial $p(x)$ is $7x^6$.
  • Question 13:
    3 pts
    		Find cubic polynomial with real coefficients having roots $x = - 2$ and $x = i$.
    $x^3+2x^2+x+2$
    $x^3+2x-4$
    $2x^3-x+14$
  • Question 14:
    3 pts
    		Polynomial of degree 4, has a root of multiplicity 2 at $x=-1$ and roots of multiplicity 1 at $x=0$ and $x=4$? The equation of polynomial is:
    $x(x+4)(x-1)^2$
    $x(x+4)(x+1)^2$
    $x(x-4)(x+1)^2$
    $x(x-4)(x-1)^2$

Basics of polynomials

Polynomials Operations

Roots of polynomials

Factoring Polynomials

Graphing Polynomials

Rational exp. operations