Worksheet: Real and Complex Roots of Polynomials

In this worksheet, consolidate your understanding of real and complex roots of polynomials.

Q1:

Are the roots of the equation real and different?

Q2:

Determine the type of the roots of the equation .

Q3:

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

Q4:

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

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 .

Q7:

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

Q8:

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

Q9:

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

Q10:

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

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?

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 ?

Q15:

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