CDS Model Paper 4 Mathematics

According to question
Let one roots of equation is alpha then others roots of equation is a2.
∴ Sum of roots =a+a2=−

(−b)

1

⇒ α(α+1)=b ...(i)
Product of roots =α.α2=

c

1

⇒ α3=c⇒α=c

1

3

...(ii)
From equations (i) and (ii),
c

1

3

(c

1

3

+1)=b ...(iii)
On cubing both sides, we get
c(c

1

3

+1)3=b3
⇒ c{c+1+3c

1

3

(c

1

3

+1)}=b3
⇒ c(c+1+3b)=b3
[from equation (iii)]
⇒ b3=3bc+c2+c