Find the condition that zeroes of polynomial $p (x) = a x^{2} + b x + c$ are reciprocal of each other.

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Solution

Given quadratic polynomial is $P (x) = a x^{2} + b x + c$
Given the roots are reciprocal to each other
Let the roots be $α, \frac{1}{α}$
$⟹$ Product of roots is $α \times \frac{1}{α} = \frac{c}{a}$
$⟹ \frac{c}{a} = 1 ⟹ c = a$

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Find the condition that zeros of polynomial p(x)= ax2 + bx + c r reciprocal of each other. Explain stepwise.

a x^{2} + b x + c = 0

f (x) = a x^{2} + b x + c, a \neq 0, c \neq 0

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β

p (x) = a x^{2} + b x + c, (a \neq 0)

= \frac{c}{a}

α

β

P (x) = a x^{2} + b x + c, \frac{1}{α} + \frac{1}{β} =

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