Which statement is correct for (x^2+\sqrt{3}x+1)?
Answer and explanation
Correct answer: It is a polynomial
A polynomial in x may have real-number coefficients, including irrational numbers such as \\(\\sqrt3\\). What matters is that the powers of x are nonnegative whole numbers and that x is not placed in a denominator or under a variable-dependent radical. In \\(x^2+\\sqrt3x+1\\), the powers are 2, 1, and 0, so it is a polynomial. Thus option A is correct.
The coefficient of x is \\(\\sqrt3\\), which is a fixed real number; it is not a variable expression. The terms have the required forms \\(x^2\\), \\(\\sqrt3x\\), and 1. Its highest nonzero power is 2, so its degree is also defined and equals 2. The presence of an irrational coefficient does not disqualify a polynomial.
Frequently asked questions
What is the correct answer to this question?
It is a polynomial
Why is this the correct answer?
A polynomial in x may have real-number coefficients, including irrational numbers such as \\(\\sqrt3\\). What matters is that the powers of x are nonnegative whole numbers and that x is not placed in a denominator or under a variable-dependent radical. In \\(x^2+\\sqrt3x+1\\), the powers are 2, 1, and 0, so it is a polynomial. Thus option A is correct.
The coefficient of x is \\(\\sqrt3\\), which is a fixed real number; it is not a variable expression. The terms have the required forms \\(x^2\\), \\(\\sqrt3x\\), and 1. Its highest nonzero power is 2, so its degree is also defined and equals 2. The presence of an irrational coefficient does not disqualify a polynomial.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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