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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=3x=3 is a root of polynomial p(x)=x2−x−6p(x) = x^2-x-6.
  • Question 2:
    1 pts
    		x=−1x=-1 is a root of polynomial p(x)=x3−x+2x+3p(x) = x^3-x+2x+3
  • Question 3:
    1 pts
    		The graph of the polynomial p(x)p(x) is given at the right. How many positive roots does p(x)p(x) has?
    0
    1
    2
    3
  • Question 4:
    2 pts
    		How many distinct roots does polynomial p(x)=(x+1)2p(x) = (x+1)^2 has

    00

    11

    22

    33

  • Question 5:
    2 pts
    		One zero of p(x)=x2+2x+2p(x) = x^2+2x+2 is 1+i1+i. Which of the following is another zero?

    ii

    i−1i-1

    1−i1-i

    −i-i

  • Question 6:
    2 pts
    		One zero of p(x)=x3−3x2+x+5p(x) = x^3- 3x^2+ x + 5 is 2−i2 - i. Which of the following is another zero?

    22

    2+i2+i

    i−2i-2

    ii

  • 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)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)p(x) has roots x=1x=1 and x=2x=2. p(x)=p(x)=
    x2−2x+1x^2-2x+1
    x2+x−4x^2+x-4
    x2−3x+2x^2-3x+2
    none of these
  • Question 9:
    3 pts
    		Polynomial p(x)p(x) has roots x=1x=1 , x=5x=5 and x=0x=0. p(x)=p(x) =
    x3−5x2+6xx^3-5x^2+6x
    x3−6x2+5xx^3-6x^2+5x
    x3−x2x^3-x^2
    none of these
  • Question 10:
    2 pts
    		Multiplicity of root x=1x=1 in polynomial p(x)=(x+1)2p(x)=(x+1)^2 is 2.
  • Question 11:
    2 pts
    		multiplicity of root x=1x=1 in polynomial p(x)=3(x−1)2(x+1)3p(x)=3(x-1)^2(x+1)^3 is 3.
  • Question 12:
    2 pts
    		Polynomial p(x)p(x), with leading coefficient 6, has a root of multiplicity 7 at x=0x=0. The equation of polynomial p(x)p(x) is 7x67x^6.
  • Question 13:
    3 pts
    		Find cubic polynomial with real coefficients having roots x=−2x = - 2 and x=ix = i.
    x3+2x2+x+2x^3+2x^2+x+2
    x3+2x−4x^3+2x-4
    2x3−x+142x^3-x+14
  • Question 14:
    3 pts
    		Polynomial of degree 4, has a root of multiplicity 2 at x=−1x=-1 and roots of multiplicity 1 at x=0x=0 and x=4x=4? The equation of polynomial is:
    x(x+4)(x−1)2x(x+4)(x-1)^2
    x(x+4)(x+1)2x(x+4)(x+1)^2
    x(x−4)(x+1)2x(x-4)(x+1)^2
    x(x−4)(x−1)2x(x-4)(x-1)^2

Basics of polynomials

Polynomials Operations

Roots of polynomials

Factoring Polynomials

Graphing Polynomials

Rational exp. operations