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If q(x) = x⁶ + x^(3/2) + 2, why is q(x) not a polynomial in x?यदि q(x) = x⁶ + x^(3/2) + 2 है, तो q(x), x का बहुपद क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because x^(3/2) has a fractional exponentBecause x^(3/2) has a fractional exponent
In a polynomial in x, every exponent of x must be a non-negative integer: 0, 1, 2, 3, and so on. The terms x⁶ and 2 satisfy this rule, but x^(3/2) has the fractional exponent 3/2. Therefore q(x) is not a polynomial in x. The number of terms and the presence of a constant do not violate the definition.x में बहुपद के प्रत्येक पद में x की घात अऋणात्मक पूर्णांक होनी चाहिए, जैसे 0, 1, 2, 3 आदि। x⁶ की घात 6 और नियतांक 2 की घात 0 है, इसलिए ये दोनों मान्य हैं। लेकिन x^(3/2) में घात 3/2 भिन्न है। इसी कारण q(x) बहुपद नहीं है; पदों की संख्या इसका कारण नहीं है।
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