Which of the following quadratic equations has roots that are reciprocals of each other?
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Answer and explanation
Correct answer: \(x^2-5x+1=0\)
If roots \(\alpha,\beta\) are reciprocals, then \(\alpha\beta=1\). For \(ax^2+bx+c=0\), their product is \(c/a\). In option A, \(c/a=1/1=1\); in B it is \(1/2\). Exam tip: check \(c/a\) directly.
Frequently asked questions
What is the correct answer to this question?
\(x^2-5x+1=0\)
Why is this the correct answer?
If roots \(\alpha,\beta\) are reciprocals, then \(\alpha\beta=1\). For \(ax^2+bx+c=0\), their product is \(c/a\). In option A, \(c/a=1/1=1\); in B it is \(1/2\). Exam tip: check \(c/a\) directly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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