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Worksheet: Real and Complex Roots of Polynomials

Q1:

Are the roots of the equation real and different?

  • Ano
  • Byes

Q2:

Determine the type of the roots of the equation .

  • Areal and different
  • Breal and equal
  • Ccomplex and not real

Q3:

Find, in its simplest form, the quadratic equation whose roots are and .

  • A
  • B
  • C
  • D
  • E

Q4:

Find, in its simplest form, the quadratic equation whose roots are and .

  • A
  • B
  • C
  • D

Q5:

If is a root of the polynomial , what is the value of ?

Q6:

Given that has a zero at and , determine the values of , , and .

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q7:

Which is the correct condition for the polynomial with real coefficients to have no non-real roots?

  • A The discriminant is equal to zero.
  • B The discriminant is positive.
  • C The discriminant is negative.
  • D The discriminant is nonnegative.
  • EThe discriminant is an integer.

Q8:

Does the polynomial , where is nonzero and all the coefficients are real, have at least one real root?

  • A cannot say
  • B no
  • C yes

Q9:

How many real roots could the polynomial have given that , and are all real?

  • A only 1
  • B 4 or 2
  • C only 2
  • D 5, 3, or 1
  • E4, 2, or 1

Q10:

If is a root of the equation , where is a polynomial with real coefficients, which other complex number must also be a root?

  • A
  • B
  • C
  • D
  • E

Q11:

How many roots does the polynomial have?

Q12:

Is it possible for a polynomial with real coefficients to have exactly 3 non-real roots?

  • A no
  • B yes

Q13:

How many roots does the polynomial have?

Q14:

If 7 and 6 are the roots of the equation , what are the values of and ?

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q15:

If the roots of the equation have a difference of 3, what is the value of ?