If \\(p\ne2\\), what must be the value of \\(p\\) for the equation \\((p-2)x^2+4x+1=0\\) to have equal roots?
Answer and explanation
Correct answer: \\(p=6\\)
Here, \\(a=p-2\\), \\(b=4\\), and \\(c=1\\). An equation has equal roots when its discriminant \\(D=b^2-4ac\\) is zero. Thus, \\(D=16-4(p-2)=24-4p=0\\), giving \\(p=6\\). The value \\(p=2\\) is not valid because it eliminates the quadratic term, so the equation is no longer quadratic. Exam tip: For equal roots, set \\(D=0\\) and also verify that \\(a\ne0\\).
Frequently asked questions
What is the correct answer to this question?
\\(p=6\\)
Why is this the correct answer?
Here, \\(a=p-2\\), \\(b=4\\), and \\(c=1\\). An equation has equal roots when its discriminant \\(D=b^2-4ac\\) is zero. Thus, \\(D=16-4(p-2)=24-4p=0\\), giving \\(p=6\\). The value \\(p=2\\) is not valid because it eliminates the quadratic term, so the equation is no longer quadratic. Exam tip: For equal roots, set \\(D=0\\) and also verify that \\(a\ne0\\).
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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