If the sum of the roots of the quadratic equation, \( a x^{2}+b x+c...

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If the sum of the roots of the quadratic equation, \( a x^{2}+b x+c=0 \) is equal to sum of the squares of their reciprocals, then prove that \( \frac{a}{c}, \frac{b}{a}, \frac{c}{b} \) are in H.P.
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