1) Given that α , β are the roots of the equation x² - 3x + a = 0 and γ , δ are the roots of the equation x² - 12x + b= 0. If α , β , γ , δ form an increasing G. P., then the ordered pair (a, b) is equal to:
A) (3 , 12) B) (12 , 3) C) (2 , 32) D) (4 , 16)
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α,β,γ,δ being G.P. they may be taken as k,kr,kr2,kr3.
S=k(1+r)=3,kr2(1+r)=12
∴3r2=12 or r=2∴k=1
P=k2r=a,k2r5=b.
Putting for r and k,a=2,b=32.
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1) Given that α , β are the roots of the equation x² - 3x + a = 0 and γ , δ are the roots of the equation x² - 12x + b= 0. If α , β , γ , δ form an increasing G. P.,
A) (3 , 12) B) (12 , 3) C) (2 , 32) D) (4 , 16)
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