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If p, q, r are in G.P. and the equations, {p}{x}^{{2}}+{2}{q}{

Question

If p, q, r are in G.P. and the equations, $p x^{2} + 2 q x + r = 0$ and $d x^{2} + 2 e x + f = 0$ have a common root, then show that $\frac{d}{p}$ , $\frac{e}{q}$ , $\frac{f}{r}$ are in A.P.

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Levi Discussed

If p, q, r are in G.P. and the equations,

p x^{2} + 2 q x + r = 0

and

d x^{2} + 2 e x + f = 0

have a common root, then show that

\frac{d}{p}

\frac{e}{q}

\frac{f}{r}

are in A.P.

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Question Text

If p, q, r are in G.P. and the equations,

p x^{2} + 2 q x + r = 0

and

d x^{2} + 2 e x + f = 0

have a common root, then show that

\frac{d}{p}

\frac{e}{q}

\frac{f}{r}

are in A.P.

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