If the two roots of the equation \(x^2-4x+k=0\) are equal, what is the value of \(k\)?
Answer and explanation
Correct answer: 4
For a quadratic equation \(ax^2+bx+c=0\) to have equal roots, its discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=1\), \(b=-4\), and \(c=k\). Thus, \((-4)^2-4(1)(k)=0\), giving \(16-4k=0\) and hence \(k=4\). Therefore, option A is correct. Exam tip: for equal roots, immediately use \(D=0\).
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a quadratic equation \(ax^2+bx+c=0\) to have equal roots, its discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=1\), \(b=-4\), and \(c=k\). Thus, \((-4)^2-4(1)(k)=0\), giving \(16-4k=0\) and hence \(k=4\). Therefore, option A is correct. Exam tip: for equal roots, immediately use \(D=0\).
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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