0 reads0 ratings0 helpful
What condition on \(u\) is necessary for the equation \(x^2-2ux+u^2+7u=0\) to have real roots?समीकरण \(x^2-2ux+u^2+7u=0\) के वास्तविक मूल होने के लिए \(u\) पर कौन-सी शर्त आवश्यक है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(u\le 0\)\(u\le 0\)
A quadratic equation has real roots when its discriminant satisfies \(D\ge 0\). Here, \(a=1\), \(b=-2u\), and \(c=u^2+7u\), so \(D=(-2u)^2-4(1)(u^2+7u)=-28u\). Thus, \(-28u\ge0\), giving \(u\le0\). Remember that \(D=0\), which gives equal real roots, is also included.द्विघात समीकरण के वास्तविक मूलों के लिए विविक्तकर \(D\ge 0\) होना चाहिए। यहाँ \(a=1\), \(b=-2u\) और \(c=u^2+7u\) हैं। इसलिए \(D=(-2u)^2-4(1)(u^2+7u)=-28u\)। अतः \(-28u\ge0\), जिससे \(u\le0\) प्राप्त होता है। ध्यान रखें कि \(D=0\) होने पर समान वास्तविक मूल भी मान्य होते हैं।
Student feedback
Was this question useful?
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Difficulty
Easy0%
Medium0%
Hard0%
Was the explanation clear?
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
