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If the remainder when the polynomial \(p(x)\) is divided by \(x-4\) is \(7\), what is the value of \(p(4)\)?यदि बहुपद \(p(x)\) को \(x-4\) से विभाजित करने पर शेषफल \(7\) है, तो \(p(4)\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(7\)\(7\)
By the Remainder Theorem, when a polynomial \(p(x)\) is divided by \(x-a\), the remainder is \(p(a)\). Here, \(a=4\) and the given remainder is \(7\), so \(p(4)=7\). The value \(0\) would apply if \(x-4\) were a factor of \(p(x)\). Exam tip: For a divisor of the form \(x-a\), substitute \(x=a\) in the polynomial.शेषफल प्रमेय के अनुसार, किसी बहुपद \(p(x)\) को \(x-a\) से विभाजित करने पर शेषफल \(p(a)\) होता है। यहाँ \(a=4\) और दिया गया शेषफल \(7\) है, इसलिए \(p(4)=7\)। विकल्प \(0\) तब होता जब \(x-4\), \(p(x)\) का गुणनखंड होता। परीक्षा-युक्ति: \(x-a\) देखकर सीधे \(p(a)\) लिखें।
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