For the equation 3x2+p x+3=0;  p>0,  if one of the roots is square of the other, then p=

Given equation is 3x2+p x+3=0 Let the roots of given equation are α and α2   ( from the given condition)Then sum of the roots  α+α2=  −  p3 ……. ( 1 )And   product of the roots  α3=1 ⇒ α=1,  ω  or  ω2. Substitute α  values in Eq. ( 1 )When  α=1,  α + α2=−p3 ⇒1+1  =  −p3 ⇒  p=−6 When  α=  ω, ⇒ω+ω2=−p3  ⇒  p=3 When α=ω2, ⇒ ω2+ω4  =  −p3  ⇒  p=3. ∴ p=3          ( ∵  by given condition p>0  )