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If α,β be the roots of the equation ax2+bx+c=0. Let Sn=αn+βn, for n1
If Δ=∣ ∣31+S11+S21+S11+S21+S31+S21+S31+S4∣ ∣, then Δ is equal to 
  1. s2(b24ac)a4
  2. (a+b+c)2(b24ac)a4
  3. b24aca4
  4. (a+b+c)24


Solution

The correct option is B (a+b+c)2(b24ac)a4
We have α,β are the roots of ax2+bx+c=0, then α+β=ba, αβ=ca
Sn=αn+βn
Δ=∣ ∣31+S11+S21+S11+S21+S31+S21+S31+S4∣ ∣
=∣ ∣ ∣31+α+β1+α2+β21+α+β1+α2+β21+α3+β31+α2+β21+α3+β31+α4+β4∣ ∣ ∣
=∣ ∣1111αβ1α2β2∣ ∣×∣ ∣1111αβ1α2β2∣ ∣
=∣ ∣1111αβ1α2β2∣ ∣2
={αβ(α+β)+1}2{(α+β)24αβ}=(ca+ba+1)2(b2a24ca)=(a+b+c)2(b24ac)a4

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