Question

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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Answer 1

Answer:

there is a answer of your question

Explanation:

(c) option is correct a=2 ,b=32

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Answer 2

Answer:

correct ans is C i.e (2,32)

Explanation:

Let α=x

β=x×r

γ=x×r ²

δ=x×r ³

As sum of roots is -b/a and product of roots is c/a

in ax ²+bx+c

So α+β=3

x+xr=3

x(1+r)=3 (1)

Similarly xr²+xr³=12

xr² (1+r)=12 (2)

Dividing (2) by (1)

r ² =4

r=2 or r=−2

Taking r=2 and substituting in (1)

x(1+2)=3

x=1

So,

α=1

β=2

γ=4

δ=8

So a=1×2 and b=4×8

Hence a=2 and b=32

So option (C) is correct answer

hope it helps you

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