Question

If the equation x³ − 3ax² + 3bx − c = 0 has positive and distinct roots, then

(A)  a² > b 

(B)  ab > c 

(C)  a³ > c 

(D)  a³ > b² > c

Answer 1

Correct option (A) a² > b

Let α,β,γ be the roots. Then α + β + γ = 3a, αβ + βγ +  γα = 3b,  αβγ  = c.

We have (α + β + γ)³ > 27 αβγ ⇒ a³ > c

Also,