Question

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)

2) Find the sum of the series upto 30 terms :

1² + 2² - 3² + 4² + 5² - 6² + 7² + 8² - 9² + ....

A) 2425 B) 2525 C) 2524 D) 2562​

Answer 1

Answer

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.

b) 2525

Step-by-step explanation:

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