Which of the following expressions is a polynomial in one variable with real coefficients?
Answer and explanation
Correct answer: \(\sqrt{2}x^2-3x+1\)
In option A, the powers of \(x\) are 2, 1, and 0, all of which are non-negative integers. Since \(\sqrt{2}\) is a real number, it is a polynomial with real coefficients. Option B contains \(x^{1/2}\), while C and D contain negative powers, so they are not polynomials. Exam tip: In a polynomial, the powers of the variable must be 0, 1, 2, 3, and so on.
Frequently asked questions
What is the correct answer to this question?
\(\sqrt{2}x^2-3x+1\)
Why is this the correct answer?
In option A, the powers of \(x\) are 2, 1, and 0, all of which are non-negative integers. Since \(\sqrt{2}\) is a real number, it is a polynomial with real coefficients. Option B contains \(x^{1/2}\), while C and D contain negative powers, so they are not polynomials. Exam tip: In a polynomial, the powers of the variable must be 0, 1, 2, 3, and so on.
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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