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If \(f(x)=x^2+px+4\) and \(g(x)=x^2-px+4\), and \((f-g)(2)=12\), what is the value of \(p\)?यदि \(f(x)=x^2+px+4\) और \(g(x)=x^2-px+4\) हैं, तथा \((f-g)(2)=12\) है, तो \(p\) का मान क्या है?
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Correct answer:सही उत्तर: 33
\((f-g)(x)=[x^2+px+4]-[x^2-px+4]=2px\). Hence, \((f-g)(2)=2p\cdot2=4p\). Given \(4p=12\), we get \(p=3\). Option 4 is incorrect because it would give \(4p=16\). Exam tip: simplify the difference of the two functions before substituting the given value of \(x\).\((f-g)(x)=[x^2+px+4]-[x^2-px+4]=2px\)। इसलिए \((f-g)(2)=2p\cdot2=4p\)। दिया है कि \(4p=12\), अतः \(p=3\)। विकल्प 4 इसलिए गलत है क्योंकि वह \(4p=16\) देगा। परीक्षा में दो फलनों का अंतर निकालते समय समान पदों को पहले काटना उपयोगी रहता है।
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