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What is the coefficient of \(x\) in the sum of the polynomials \(p(x)=4x^3-7x^2+2x-5\) and \(q(x)=-x^3+3x^2-6x+9\)?बहुपदों \(p(x)=4x^3-7x^2+2x-5\) और \(q(x)=-x^3+3x^2-6x+9\) के योग में \(x\) का गुणांक क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: -4-4
The coefficients of \(x\) in the two polynomials are \(2\) and \(-6\), respectively. Therefore, the coefficient of \(x\) in their sum is \(2+(-6)=-4\). The complete sum is \(3x^3-4x^2-4x+4\). Exam tip: when adding polynomials, combine coefficients only for terms with the same power.दोनों बहुपदों में \(x\) के गुणांक क्रमशः \(2\) और \(-6\) हैं। अतः योग में \(x\) का गुणांक \(2+(-6)=-4\) होगा। वास्तव में पूरा योग \(3x^3-4x^2-4x+4\) है। परीक्षा-युक्ति: बहुपदों को जोड़ते समय केवल समान घात वाले पदों के गुणांक जोड़ें।
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