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Reena says that \(5x^2-3\sqrt{x}+1\) is a polynomial in \(x\). What is her mistake?रीना कहती है कि \(5x^2-3\sqrt{x}+1\) , \(x\) का बहुपद है। उसकी गलती क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: In \(\sqrt{x}\), the exponent of \(x\) is \(\frac{1}{2}\), which is not a non-negative integer.\(\sqrt{x}\) में \(x\) का घातांक \(\frac{1}{2}\) है, जो गैर-ऋणात्मक पूर्णांक नहीं है।
In a polynomial, variable exponents must be non-negative integers such as \(0,1,2,\ldots\). Here, \(\sqrt{x}=x^{1/2}\), so the expression is not a polynomial. Exam tip: rewrite radicals as fractional powers to check quickly.बहुपद में चर के घातांक \(0,1,2,\ldots\) जैसे गैर-ऋणात्मक पूर्णांक होते हैं। यहाँ \(\sqrt{x}=x^{1/2}\) है, इसलिए यह बहुपद नहीं है। परीक्षा टिप: मूल चिह्न को भिन्न घातांक में बदलकर जाँचें।
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