If the quadratic equation \(px^2+4x+1=0\) has equal roots and \(p\neq 0\), what is the value of \(p\)?
Answer and explanation
Correct answer: 4
For equal roots, the discriminant \(D=b^2-4ac\) must be zero. Here, \(a=p\), \(b=4\), and \(c=1\), so \(D=4^2-4(p)(1)=0\), giving \(16-4p=0\) and hence \(p=4\). Option B has the wrong sign, while \(p=4\) also satisfies \(p\neq 0\), keeping the equation quadratic. Exam tip: For equal roots, immediately use \(D=0\).
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, \(a=p\), \(b=4\), and \(c=1\), so \(D=4^2-4(p)(1)=0\), giving \(16-4p=0\) and hence \(p=4\). Option B has the wrong sign, while \(p=4\) also satisfies \(p\neq 0\), keeping the equation quadratic. Exam tip: For equal roots, immediately use \(D=0\).
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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