Find the condition that zeroes of polynomial $p( x)=ax^2+bx+c$ are reciprocal of each other.
Given: Zeroes of polynomial $p( x)=ax^2+bx+c$ are reciprocal of each other.
To do: To find the condition that zeroes of polynomial $p( x)=ax^2+bx+c$ are reciprocal of each other.
Solution:
Given polynomial: $p( x)=ax^2+bx+c$
Let $\alpha$ and $\frac{1}{\alpha}$ are the zeroes of the given polynomial.
Therefore, sum of the zeroes$=\alpha+\frac{1}{\alpha}=-\frac{b}{a}$
Product of the zeroes$=\alpha.\frac{1}{\alpha}=\frac{c}{a}$
$\Rightarrow 1=\frac{c}{a}$
$\Rightarrow c=a$
Thus, for $c=a$ zeroes of the polynomial $p( x)=ax^2+bx+c$ are reciprocal of each other.
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