Class 11 Mathematics · Chapter 1 · Test 2
Polynomials and Unity Roots
40 MCQs This test covers factorization of complex polynomials, the fundamental theorem of algebra, and solving quadratics by completing the square. It also covers building polynomials from given zeros, cube roots and fourth roots of unity with their properties, and the roots of numbers like -8, 64 and 625.
40 questions · 35 min · 40 marks
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Sample questions
The first 5 of 40. Try each one, then tap to see the answer.
Question 1
A polynomial of degree n ≥ 1 has exactly how many roots in C?
- An - 1
- Bn
- Cn + 1
- D2n
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Answer: B
This is the fundamental theorem of algebra.
Question 2
a^2 + 4b^2 factorizes over C as:
- A(a - 2bi)(a + 2bi)
- B(a - 4bi)(a + 4bi)
- C(a + 2b)(a - 2b)
- D(a - 2b)^2
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Answer: A
a^2 - (2bi)^2 = a^2 + 4b^2.
Question 3
9a^2 + 16b^2 factorizes over C as:
- A(3a - 16bi)(3a + 16bi)
- B(9a - 4bi)(9a + 4bi)
- C(3a - 4bi)(3a + 4bi)
- D(3a + 4b)^2
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Answer: C
(3a)^2 - (4bi)^2 = 9a^2 + 16b^2.
Question 4
z^2 + 4z + 5 factorizes as:
- A(z - 2 + i)(z - 2 - i)
- B(z + 4 + i)(z + 4 - i)
- C(z + 2)(z + 2)
- D(z + 2 + i)(z + 2 - i)
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Answer: D
(z + 2)^2 - i^2 = z^2 + 4z + 5.
Question 5
z^2 + 6z + 13 factorizes as:
- A(z - 3 + 2i)(z - 3 - 2i)
- B(z + 3 + 2i)(z + 3 - 2i)
- C(z + 3 + 4i)(z + 3 - 4i)
- D(z + 6 + i)(z + 6 - i)
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Answer: B
(z + 3)^2 - (2i)^2 = z^2 + 6z + 13.
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