Q. Which of the following is a correct representation of a quadratic polynomial?
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A.
x^2 + 2x + 1
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B.
x^3 + 3x^2 + 3x + 1
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C.
2x + 3
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D.
x^4 - x^2 + 1
Solution
A quadratic polynomial is defined as a polynomial of degree 2, which is represented by x^2 + 2x + 1.
Correct Answer:
A
— x^2 + 2x + 1
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Q. Which of the following is a root of the polynomial P(x) = x^2 - 5x + 6?
Solution
The roots of the polynomial can be found by factoring it as (x-2)(x-3) = 0, giving roots 2 and 3.
Correct Answer:
B
— 2
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Q. Which of the following is true about the roots of a polynomial of odd degree?
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A.
It has an even number of roots.
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B.
It has at least one real root.
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C.
It has no real roots.
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D.
It has exactly two real roots.
Solution
A polynomial of odd degree must have at least one real root due to the Intermediate Value Theorem.
Correct Answer:
B
— It has at least one real root.
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Q. Which of the following is true about the roots of the polynomial P(x) = x^2 + 4x + 4?
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A.
It has two distinct real roots.
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B.
It has one real root with multiplicity 2.
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C.
It has no real roots.
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D.
It has two complex roots.
Solution
The polynomial can be factored as (x + 2)^2, indicating it has one real root with multiplicity 2.
Correct Answer:
B
— It has one real root with multiplicity 2.
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Q. Which of the following is true about the roots of the polynomial x^2 + 4x + 4?
-
A.
It has two distinct real roots.
-
B.
It has one real root with multiplicity 2.
-
C.
It has no real roots.
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D.
It has two complex roots.
Solution
The polynomial can be factored as (x + 2)(x + 2), indicating it has one real root with multiplicity 2.
Correct Answer:
B
— It has one real root with multiplicity 2.
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Q. Which of the following polynomials is a perfect square?
-
A.
x^2 + 4x + 4
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B.
x^2 - 4
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C.
x^2 + 2x + 3
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D.
x^2 - 2x + 1
Solution
The polynomial x^2 + 4x + 4 can be factored as (x + 2)^2, making it a perfect square.
Correct Answer:
A
— x^2 + 4x + 4
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Q. Which of the following polynomials is a quadratic polynomial?
-
A.
x^3 - 2x + 1
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B.
2x^2 + 3x - 5
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C.
4x + 7
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D.
x^4 - x^2 + 1
Solution
A quadratic polynomial is defined as a polynomial of degree 2, which is 2x^2 + 3x - 5.
Correct Answer:
B
— 2x^2 + 3x - 5
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Q. Which of the following terms best describes a polynomial with more than one variable?
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A.
Univariate polynomial
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B.
Multivariate polynomial
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C.
Constant polynomial
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D.
Linear polynomial
Solution
A polynomial that contains more than one variable is referred to as a multivariate polynomial.
Correct Answer:
B
— Multivariate polynomial
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Q. Which of the following terms is NOT a polynomial?
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A.
5x^2 + 3x - 7
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B.
2x^3 - 4x + 1
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C.
3/x + 2
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D.
x^4 + 2x^2 + 1
Solution
The term 3/x is not a polynomial because it contains a negative exponent when rewritten as 3x^(-1).
Correct Answer:
C
— 3/x + 2
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Q. Which of the following terms is used to describe a polynomial with exactly one term?
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A.
Binomial
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B.
Trinomial
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C.
Monomial
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D.
Polynomial
Solution
A polynomial with exactly one term is called a monomial.
Correct Answer:
C
— Monomial
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