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For the equation \(x^2-8x+m=0\), what is the value of \(m\) if its roots are real and equal?समीकरण \(x^2-8x+m=0\) में यदि इसके मूल (roots) वास्तविक और बराबर (equal) हैं, तो \(m\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(m=16\)\(m=16\)
For real and equal roots, the discriminant must be \(\Delta=0\). For \(x^2-8x+m=0\), we have \(a=1,\;b=-8,\;c=m\). So \(\Delta=b^2-4ac=(-8)^2-4(1)(m)=64-4m\). Set \(64-4m=0\Rightarrow 4m=64\Rightarrow m=16\).वास्तविक और बराबर मूलों (equal roots) के लिए विस्क्रिमिनेंट \(\Delta=0\) होना चाहिए। \(x^2-8x+m=0\) में \(a=1,\;b=-8,\;c=m\) है। अतः \(\Delta=b^2-4ac=(-8)^2-4(1)(m)=64-4m\)। अब \(64-4m=0\Rightarrow 4m=64\Rightarrow m=16\).
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