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If the polynomial \(f(x)=x^2+ax+b\) satisfies \(f(0)=-8\) and \(f(4)=0\), what is the value of \(a\)?यदि बहुपद \(f(x)=x^2+ax+b\) के लिए \(f(0)=-8\) और \(f(4)=0\) है, तो \(a\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: -2-2
Since \(f(0)=b\), we get \(b=-8\). Substituting \(x=4\) in the second condition gives \(16+4a-8=0\), so \(4a+8=0\) and hence \(a=-2\). Exam tip: use the condition at \(x=0\) first to find the constant term, then use the other condition to determine the unknown coefficient.\(f(0)=b\) होने से \(b=-8\)। अब \(f(4)=0\) रखने पर \(16+4a-8=0\), अर्थात् \(4a+8=0\)। इसलिए \(a=-2\)। परीक्षा-युक्ति: पहले \(x=0\) रखकर अचर पद ज्ञात करें, फिर दूसरी शर्त से अज्ञात गुणांक निकालें।
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