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If \(p(x)=x^3+ax+b\), \(p(1)=6\), and \(p(-2)=-9\), what is the value of \(a\)?यदि \(p(x)=x^3+ax+b\), \(p(1)=6\) और \(p(-2)=-9\) है, तो \(a\) का मान क्या है?
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Correct answer:सही उत्तर: 22
Substituting \(x=1\) gives \(1+a+b=6\), so \(a+b=5\). Substituting \(x=-2\) gives \(-8-2a+b=-9\), so \(-2a+b=-1\). Subtracting the second equation from the first yields \(3a=6\), hence \(a=2\). Therefore, option B is correct. Exam tip: when substituting a negative value in a cubic polynomial, carefully retain the sign of \((-2)^3=-8\).\(p(1)=6\) रखने पर \(1+a+b=6\), अर्थात् \(a+b=5\)। इसी प्रकार, \(p(-2)=-9\) से \(-8-2a+b=-9\), अर्थात् \(-2a+b=-1\) मिलता है। दोनों समीकरणों को घटाने पर \(3a=6\), इसलिए \(a=2\)। अतः सही विकल्प B है। परीक्षा-युक्ति: घन बहुपद में ऋणात्मक मान रखने पर \((-2)^3=-8\) का चिन्ह अवश्य जाँचें।
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