If p,q,r are the roots of the equation ax^3 + bx^2 + cx + d = 0. then find equation whose roots are a] pq,qr,pr b] [pq]^2,[qr]^2,[pr]^2 c] p[q+r],q[p+r],r[p+q] d] pq+1/r,qr+1/p,pr+1/q e] p-1/qr,q-1/rp,r-1/pq

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$I f P (Q - r) x^{2} + Q (r - P) x + r (P - Q) = 0 h a s e q u a l r o o t s t h e n \frac{2}{Q} = (w h e r e P, Q, r ϵ R)$

If $p > q > 0 a n d p r < - 1 < q r$ , then find the value of

{tan}^{- 1} \frac{p - q}{1 + p q} + {tan}^{- 1} \frac{q - r}{1 + q r} + {tan}^{- 1} \frac{r - p}{1 + r p} .

p, q, r

p + q + r = 0, a (q r + r p + p q) = 2 a - x, a p q r = y, q r = 1

(p q - q r + p r) (p q + q r) - (p r + p q) (p + q - r)

p (q - r) x^{2} + q (r - p) x + r (p - q) = 0

\frac{1}{p} + \frac{1}{r} = \frac{2}{q} = \frac{m}{q}

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