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A student says that the polynomial \(R(x)=3x^4-2x^3+x^2+5x^4+2x^3-8x^4\) has degree 4 because an \(x^4\) term is visible in it. Which is the correct evaluation of the student's statement?एक विद्यार्थी कहता है कि बहुपद \(R(x)=3x^4-2x^3+x^2+5x^4+2x^3-8x^4\) की डिग्री 4 है, क्योंकि इसमें \(x^4\) पद दिखाई देता है। उसके कथन का सही मूल्यांकन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: The student is incorrect; after combining like terms, the \(x^4\) and \(x^3\) terms cancel, so the degree is 2.विद्यार्थी गलत है; समान पदों को मिलाने पर \(x^4\) और \(x^3\) पद कट जाते हैं, इसलिए बहुपद की डिग्री 2 है।
The coefficient of \(x^4\) is \(3+5-8=0\), and that of \(x^3\) is \(-2+2=0\). Thus \(R(x)=x^2\), whose degree is 2. In exams, simplify before finding degree.\(x^4\) का गुणांक \(3+5-8=0\) और \(x^3\) का गुणांक \(-2+2=0\) है। अतः \(R(x)=x^2\), जिसकी डिग्री 2 है। परीक्षा में पहले समान पद मिलाइए।
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