Let α=a,β=ar,γ=ar2,δ=ar3
α+β=3⇒a+ar=3 ...........(1)
γ+δ=6⇒ar2+ar3=6 .........(2)
By (1) and (2) ⇒a(1+r)ar2(1+r)=36
⇒r2=2
∴ 2q−p2q+p=2γδ−αβ2γδ+αβ=2a2r5−a2r2a2r5+a2r=2r4−12r4+1=8−18+1=79
Let α and β be the roots of x2−3x+p=0 and γ and δ be the roots of x2−6x+q=0. If α,β,γ,δ from a geometric progression. Then ratio (2q+p):(2q−p) is
Held on 4 Sept 2020 · Verified 6 Jul 2026.
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