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

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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Answer 2

Answer:

α,β,γ,δ being G.P. they may be taken ask, kr,kr²,kr³

S=k(1+r)=3

kr² (1+r)=12

∴3r² =12 or r=2∴k=1

P=k²r=ak

2

r

5 =b.

Putting for r and k,a=2,b=32.