For the two roots of the equation \(x^2-(r+4)x+4r=0\) to be equal, what must be the value of \(r\)?
Answer and explanation
Correct answer: \(r=4\)
For a quadratic equation \(ax^2+bx+c=0\), equal roots occur when the discriminant \(D=b^2-4ac\) is zero. Here, \(a=1\), \(b=-(r+4)\), and \(c=4r\), so \(D=(r+4)^2-16r=(r-4)^2\). Setting \(D=0\) gives \((r-4)^2=0\), hence \(r=4\). Exam tip: whenever a question asks for equal roots, begin with the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
\(r=4\)
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\), equal roots occur when the discriminant \(D=b^2-4ac\) is zero. Here, \(a=1\), \(b=-(r+4)\), and \(c=4r\), so \(D=(r+4)^2-16r=(r-4)^2\). Setting \(D=0\) gives \((r-4)^2=0\), hence \(r=4\). Exam tip: whenever a question asks for equal roots, begin with 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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