If \(k\neq 0\) and \(kx^2-2(k+1)x+(k+3)=0\) is a quadratic equation, what must be the value of \(k\) for it to have equal roots?
Answer and explanation
Correct answer: \(k=1\)
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=-2(k+1)\), and \(c=k+3\). Therefore, \(D=4(k+1)^2-4k(k+3)=4(1-k)\). Setting \(D=0\) gives \(k=1\), which also satisfies \(k\neq0\). Exam tip: For equal roots of a quadratic equation, apply \(D=0\) directly.
Frequently asked questions
What is the correct answer to this question?
\(k=1\)
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=-2(k+1)\), and \(c=k+3\). Therefore, \(D=4(k+1)^2-4k(k+3)=4(1-k)\). Setting \(D=0\) gives \(k=1\), which also satisfies \(k\neq0\). Exam tip: For equal roots of a quadratic equation, apply \(D=0\) directly.
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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