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If the quadratic equation \(kx^2+10x+5=0\) has equal roots and \(k\ne0\), what is the value of \(k\)?
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Answer and explanation
Correct answer: 5
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=10\), and \(c=5\), so \(10^2-4(k)(5)=0\). Thus, \(100-20k=0\), giving \(k=5\). Exam tip: For equal roots of a quadratic equation, set the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=10\), and \(c=5\), so \(10^2-4(k)(5)=0\). Thus, \(100-20k=0\), giving \(k=5\). Exam tip: For equal roots of a quadratic equation, set the discriminant equal to zero.
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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