What is the correct discriminant \(D\) of the quadratic equation \(x^2-2(k+1)x+k^2=0\)?
Answer and explanation
Correct answer: \(4(2k+1)\)
Here, \(a=1\), \(b=-2(k+1)\), and \(c=k^2\). Hence, \(D=b^2-4ac=4(k+1)^2-4k^2=4[(k+1)^2-k^2]=4(2k+1)\). Option B ignores the terms involving \(k\), while option D omits the constant term \(4\). Exam tip: identify \(a,b,c\) carefully before applying the discriminant formula, and simplify only afterward.
Frequently asked questions
What is the correct answer to this question?
\(4(2k+1)\)
Why is this the correct answer?
Here, \(a=1\), \(b=-2(k+1)\), and \(c=k^2\). Hence, \(D=b^2-4ac=4(k+1)^2-4k^2=4[(k+1)^2-k^2]=4(2k+1)\). Option B ignores the terms involving \(k\), while option D omits the constant term \(4\). Exam tip: identify \(a,b,c\) carefully before applying the discriminant formula, and simplify only afterward.
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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