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Step-by-step explanation: answer is (2)
alpha-a, beta-b, gamma-c
a+b+c=0
ab+bc+ac=2
abc= 3
Now for new equation,
(a²+b²)/ab, (b²+c²)/bc, (c²+a²)/ac
(a²+b²=(a+b)²-2ab=c²-2ab)
sum of roots= (a³+b³+c³-6abc)/3=-3
Now, (a²+b²)/ab=(c²-2ab)/ab=(c²/ab-2)=(c³/3-2))
So Product of roots=(c³-6)(b³-6)(a³-6)/27 =-75/27
Some formula used:
(a³+b³+c³=(a+b+c)³+3abc=9)
[a³b³+b³c³+a³c³=2³-3abc(a+c)(b+c)(a+b)=8+27=35]
Hence answer will be (2) x=(-3/2)(1+y). As this will give new equation will sum of roots as -3 and product as (-75/27)
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