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 ?