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A student says that both \(4x^3-2x+1\) and \(x^{1/2}+3\) are polynomials. Why is the statement incorrect?एक विद्यार्थी कहता है कि \(4x^3-2x+1\) और \(x^{1/2}+3\) दोनों बहुपद हैं। उसका कथन गलत क्यों है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: In \(x^{1/2}+3\), the exponent of the variable is \(1/2\), which is not a non-negative integer.\(x^{1/2}+3\) में चर की घात \(1/2\) है, जो ऋणेतर पूर्णांक नहीं है।
In a polynomial, every variable exponent must be a non-negative integer such as \(0,1,2,\dots\). Since \(x^{1/2}\) has exponent \(1/2\), it is not a polynomial. Negative coefficients are allowed. Exam tip: check exponents first.बहुपद में चर की प्रत्येक घात \(0,1,2,\dots\) जैसी ऋणेतर पूर्णांक होनी चाहिए। \(x^{1/2}\) की घात \(1/2\) है, इसलिए यह बहुपद नहीं है। ऋणात्मक गुणांक मान्य हैं। परीक्षा टिप: घात पहले जाँचें।
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