If the quadratic equation \(x^2+2(k-1)x+k+5=0\) has equal roots, what are the possible values of \(k\)?
Answer and explanation
Correct answer: 4 and −1
For equal roots, the discriminant must be zero. Here, \(a=1\), \(b=2(k-1)\), and \(c=k+5\). Thus, \(D=[2(k-1)]^2-4(1)(k+5)=4(k^2-3k-4)=0\). Factoring gives \((k-4)(k+1)=0\), so \(k=4\) or \(k=-1\). The distractors arise from sign or factorisation errors. Exam tip: whenever a quadratic has equal roots, immediately apply \(D=0\).
Frequently asked questions
What is the correct answer to this question?
4 and −1
Why is this the correct answer?
For equal roots, the discriminant must be zero. Here, \(a=1\), \(b=2(k-1)\), and \(c=k+5\). Thus, \(D=[2(k-1)]^2-4(1)(k+5)=4(k^2-3k-4)=0\). Factoring gives \((k-4)(k+1)=0\), so \(k=4\) or \(k=-1\). The distractors arise from sign or factorisation errors. Exam tip: whenever a quadratic has equal roots, immediately apply \(D=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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