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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 ?
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