JEE Main 20248 Apr, Evening shiftMathematicsEasyLimit, Continuity and Differentiability420× since 2002If the function f(x)=2x3−9ax2+12a2x+1,a>0f(x)=2 x^3-9 \mathrm{ax}^2+12 \mathrm{a}^2 x+1, \mathrm{a}> 0f(x)=2x3−9ax2+12a2x+1,a>0 has a local maximum at x=αx=\alphax=α and a local minimum at x=α2x=\alpha^2x=α2, then α\alphaα and α2\alpha^2α2 are the roots of the equation :AOption A. x2−6x+8=0x^2-6 x+8=0x2−6x+8=0BOption B. 8x2−6x+1=08 x^2-6 x+1=08x2−6x+1=0COption C. 8x2+6x−1=08 x^2+6 x-1=08x2+6x−1=0DOption D. x2+6x+8=0x^2+6 x+8=0x2+6x+8=0CheckSkip · show solution
