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Which statement is always true about the degree of the product of two non-zero polynomials?दो अशून्य बहुपदों के गुणनफल की डिग्री के बारे में कौन-सा कथन सदैव सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: The degree of the product equals the sum of the degrees of the two polynomials.गुणनफल की डिग्री दोनों बहुपदों की डिग्रियों के योग के बराबर होती है
If the leading terms of non-zero polynomials are \(ax^m\) and \(bx^n\), their product has leading term \(abx^{m+n}\). Hence its degree is \(m+n\), not the larger degree. Exam tip: note the non-zero condition.यदि अशून्य बहुपदों के अग्र पद क्रमशः \(ax^m\) और \(bx^n\) हैं, तो गुणनफल का अग्र पद \(abx^{m+n}\) होगा। अतः डिग्री \(m+n\) होती है। परीक्षा में ‘अशून्य’ शर्त अवश्य देखें।
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