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For the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), when will its roots be reciprocals of each other?
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Answer and explanation
Correct answer: When \(c=a\)
If the roots are \(\alpha\) and \(\beta\), then \(\alpha\beta=\frac{c}{a}\). Reciprocal roots have product \(1\), so \(c=a\). The condition \(b=0\) indicates additive inverse roots instead. Exam tip: use \(c/a\) for the product of roots.
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What is the correct answer to this question?
When \(c=a\)
Why is this the correct answer?
If the roots are \(\alpha\) and \(\beta\), then \(\alpha\beta=\frac{c}{a}\). Reciprocal roots have product \(1\), so \(c=a\). The condition \(b=0\) indicates additive inverse roots instead. Exam tip: use \(c/a\) for the product of roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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