How to prove the roots of $ax^2 + bx + a$ are reciprocals of each other? I tried using quadratic formula to find the two roots but got stuck at the part on how to prove they are reciprocal.
Please offer some help, thanks!
2026-03-25 14:35:55.1774449355
How to prove the roots of $ax^2 + bx + a$ are reciprocals of each other?
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Let $\alpha\neq 0$ be a root. Then, $a\alpha^2+b\alpha +a=0$. If you divide the equation by $\alpha^2$, you will get
$$\frac{a}{\alpha^2}+\frac{b}{\alpha}+a=0$$
What does the previous equation imply?