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Question: Answered & Verified by Expert
If $\alpha$ and $\beta$ are the roots ofthe equation $a x^{2}+b x+c=0$, then what are the roots of the equation $c x^{2}+b x+a=0 ?$
MathematicsQuadratic EquationNDANDA 2007 (Phase 2)
Options:
  • A $\beta, \frac{1}{\alpha}$
  • B $\alpha, \frac{1}{\beta}$
  • C $-\alpha,-\beta$
  • D $\frac{1}{\alpha}, \frac{1}{\beta}$
Solution:
1101 Upvotes Verified Answer
The correct answer is: $\frac{1}{\alpha}, \frac{1}{\beta}$
As given, $\alpha$, and $\beta$ are the roots of $a x^{2}+b x+c=0$, then the roots of $\mathrm{cx}^{2}+\mathrm{bx}+\mathrm{a}=0$ will be reciprocal of $\alpha$ and $\beta$, i.e., $\frac{1}{\alpha}$ and $\frac{1}{\beta}$.

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