If the quadratic equation \(kx^2+8x+4=0\) has equal roots and \(k\neq0\), what is the value of \(k\)?
Answer and explanation
Correct answer: 4
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=8\), and \(c=4\). Thus, \(D=8^2-4(k)(4)=0\), giving \(64-16k=0\) and hence \(k=4\). Values such as 8 or 16 do not make the discriminant zero. Exam tip: For a quadratic equation with equal roots, set the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=k\), \(b=8\), and \(c=4\). Thus, \(D=8^2-4(k)(4)=0\), giving \(64-16k=0\) and hence \(k=4\). Values such as 8 or 16 do not make the discriminant zero. Exam tip: For a quadratic equation with equal roots, 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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