For the equation \(x^2-2(k+2)x+9=0\) to have equal roots, what are the possible values of \(k\)?
Answer and explanation
Correct answer: \(k=1\) या \(k=-5\)
A quadratic equation \(ax^2+bx+c=0\) has equal roots when its discriminant \(D=b^2-4ac\) is zero. Here, \(a=1\), \(b=-2(k+2)\), and \(c=9\). Thus, \(D=4(k+2)^2-36=0\), giving \((k+2)^2=9\) and hence \(k+2=\pm3\). Therefore, \(k=1\) or \(k=-5\). Exam tip: For equal-root questions, immediately apply the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(k=1\) या \(k=-5\)
Why is this the correct answer?
A quadratic equation \(ax^2+bx+c=0\) has equal roots when its discriminant \(D=b^2-4ac\) is zero. Here, \(a=1\), \(b=-2(k+2)\), and \(c=9\). Thus, \(D=4(k+2)^2-36=0\), giving \((k+2)^2=9\) and hence \(k+2=\pm3\). Therefore, \(k=1\) or \(k=-5\). Exam tip: For equal-root questions, immediately apply the condition \(D=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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