In which option are all coefficients real and powers of (x) valid?
Answer and explanation
Correct answer: \(2x^3-\pi x^2+\sqrt{13}\)
In a polynomial, the exponent of the variable \(x\) must be a non-negative integer, while coefficients may be any real numbers. In option A, \(2\), \(-\pi\), and \(\sqrt{13}\) are real coefficients, and the exponents of \(x\) are \(3\), \(2\), and \(0\). Option B has exponent \(-\sqrt{2}\), option C has exponent \(\frac{1}{2}\), and option D has exponent \(-1\); hence they are not polynomials. Exam tip: When \(x\) is under a root or in a denominator, check its exponent first.
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What is the correct answer to this question?
\(2x^3-\pi x^2+\sqrt{13}\)
Why is this the correct answer?
In a polynomial, the exponent of the variable \(x\) must be a non-negative integer, while coefficients may be any real numbers. In option A, \(2\), \(-\pi\), and \(\sqrt{13}\) are real coefficients, and the exponents of \(x\) are \(3\), \(2\), and \(0\). Option B has exponent \(-\sqrt{2}\), option C has exponent \(\frac{1}{2}\), and option D has exponent \(-1\); hence they are not polynomials. Exam tip: When \(x\) is under a root or in a denominator, check its exponent first.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Definition of a Polynomial.
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