if two roots of 20x3−16x2+x+1=0  are equal, then the roots are

Let the given equation is f(x)=20x3−16x2+x+1=0 Let α,β,γ  are the roots of the equation  ⇒f'(x)=60x2−32x+1=0 Substitute x=12 ⇒f'(12)=60(12)2−32(12)+1=0 And f(12)=0 ∴  12 is one root.⇒α=12 By the given condition, two roots of the equation are equal⇒α=β=12 Now the product of the roots : αβγ=−120 ⇒12(12)γ=−120 ⇒γ=−15 ∴  Roots are 12,12,−15  Hence (1) is correct choice