If the quadratic equation \(kx^2-22x+121=0\) has equal roots, what is the value of \(k\)?
Answer and explanation
Correct answer: 1
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=-22\), and \(c=121\), so \(D=(-22)^2-4(k)(121)=484-484k\). Setting this equal to zero gives \(k=1\). Therefore, option A is correct. Exam tip: identify \(a\), \(b\), and \(c\) carefully before applying \(D=0\).
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=-22\), and \(c=121\), so \(D=(-22)^2-4(k)(121)=484-484k\). Setting this equal to zero gives \(k=1\). Therefore, option A is correct. Exam tip: identify \(a\), \(b\), and \(c\) carefully before applying \(D=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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