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For which value of \(a\) will the equation \(x^2-(a+3)x+3a=0\) have equal roots?किस मान के लिए समीकरण \(x^2-(a+3)x+3a=0\) के दोनों मूल समान होंगे?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(a=3\)\(a=3\)
A quadratic has equal roots when its discriminant is zero. Here, \(A=1\), \(B=-(a+3)\), and \(C=3a\), so \(D=B^2-4AC=(a+3)^2-12a=(a-3)^2\). Setting \(D=0\) gives \((a-3)^2=0\), hence \(a=3\).द्विघात समीकरण के दोनों मूल समान होते हैं जब उसका विविक्तकर शून्य हो। यहाँ \(A=1\), \(B=-(a+3)\) और \(C=3a\), इसलिए \(D=B^2-4AC=(a+3)^2-12a=(a-3)^2\)। \(D=0\) रखने पर \((a-3)^2=0\), अतः \(a=3\)।
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