Which statement is correct about (x^2 + 1)/2?
Answer and explanation
Correct answer: It is a polynomial
The governing criterion is the definition of a polynomial in one variable: it is a finite sum of non-negative integral powers of the variable multiplied by coefficients from the specified number system. Dividing the entire expression by 2 gives (x^2 + 1)/2 = (1/2)x^2 + 1/2. This is a sum of x^2 and a constant, and both coefficients, 1/2 and 1/2, are real numbers. Hence it is a polynomial in x, with degree 2. Option A is correct. A denominator does not automatically prevent an expression from being a polynomial; the problem would arise if x occurred in a denominator or with a negative or fractional exponent. Only x appears, so it does not have two variables. Its degree is also defined because the polynomial is non-zero.
Frequently asked questions
What is the correct answer to this question?
It is a polynomial
Why is this the correct answer?
The governing criterion is the definition of a polynomial in one variable: it is a finite sum of non-negative integral powers of the variable multiplied by coefficients from the specified number system. Dividing the entire expression by 2 gives (x^2 + 1)/2 = (1/2)x^2 + 1/2. This is a sum of x^2 and a constant, and both coefficients, 1/2 and 1/2, are real numbers. Hence it is a polynomial in x, with degree 2. Option A is correct. A denominator does not automatically prevent an expression from being a polynomial; the problem would arise if x occurred in a denominator or with a negative or fractional exponent. Only x appears, so it does not have two variables. Its degree is also defined because the polynomial is non-zero.
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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