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For which value of \(a\) will the polynomial \(P(x)=(a-3)x^5+2x^3-1\) be a cubic polynomial?किस मान के लिए बहुपद \(P(x)=(a-3)x^5+2x^3-1\) एक घन बहुपद होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a=3\)\(a=3\)
A cubic polynomial must have highest power 3. Thus, the coefficient of \(x^5\) must be zero: \(a-3=0\), so \(a=3\). Then \(P(x)=2x^3-1\). Exam tip: ignore any term whose coefficient becomes zero.घन बहुपद की उच्चतम घात 3 होनी चाहिए। इसलिए \(x^5\) का गुणांक शून्य होगा: \(a-3=0\), अतः \(a=3\)। तब \(P(x)=2x^3-1\) है। परीक्षा टिप: डिग्री तय करते समय शून्य गुणांक वाले पद को छोड़ दें।
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