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If \(p(x)=x^2+kx+6\) and \(p(2)=0\), what is the value of \(k\)?यदि \(p(x)=x^2+kx+6\) और \(p(2)=0\) है, तो \(k\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: -5-5
Since \(p(2)=0\), substitute \(x=2\) into the polynomial: \(2^2+2k+6=0\), so \(4+2k+6=0\). Hence \(2k=-10\) and \(k=-5\). Therefore, option A is correct. Exam tip: whenever a zero of a polynomial is given, substitute it for \(x\) and set the polynomial equal to zero.क्योंकि \(p(2)=0\), इसलिए \(2^2+2k+6=0\), अर्थात \(4+2k+6=0\)। इससे \(2k=-10\) और \(k=-5\) प्राप्त होता है। अतः सही उत्तर A है। परीक्षा-युक्ति: किसी शून्यक का मान दिया हो, तो उसे बहुपद में रखकर समीकरण बनाइए।
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