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For which values of \(k\) will the quadratic equation \(x^2-2(k+1)x+(k^2+1)=0\) have two distinct real roots?
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Answer and explanation
Correct answer: \(k>0\)
The discriminant is \(D=[-2(k+1)]^2-4(k^2+1)=8k\). Distinct real roots require \(D>0\), so \(k>0\). At \(k=0\), the roots are equal. Exam tip: check the sign of the discriminant.
Frequently asked questions
What is the correct answer to this question?
\(k>0\)
Why is this the correct answer?
The discriminant is \(D=[-2(k+1)]^2-4(k^2+1)=8k\). Distinct real roots require \(D>0\), so \(k>0\). At \(k=0\), the roots are equal. Exam tip: check the sign of the discriminant.
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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