For the quadratic equation \(ax^2+bx+c=0\), where \(a\neq0\) and \(c\neq0\), which condition is necessary and sufficient for its two roots to be reciprocals of each other?
Answer and explanation
Correct answer: \(a=c\)
Let the roots be \(\alpha,\beta\). Reciprocal roots must satisfy \(\alpha\beta=1\). By Vieta’s formula, \(\alpha\beta=c/a\), so \(c/a=1\Rightarrow a=c\). The condition \(b=0\) only makes the sum of roots zero. Exam tip: check the product first for reciprocal roots.
Frequently asked questions
What is the correct answer to this question?
\(a=c\)
Why is this the correct answer?
Let the roots be \(\alpha,\beta\). Reciprocal roots must satisfy \(\alpha\beta=1\). By Vieta’s formula, \(\alpha\beta=c/a\), so \(c/a=1\Rightarrow a=c\). The condition \(b=0\) only makes the sum of roots zero. Exam tip: check the product first for reciprocal 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
