If the function {\f}( {\x})=2 {\x}^3-9 {\ax}^2+12 {\a}^2 {\x}+1, {\a} > 0 has a local maximum at {\x}=\alpha and a local minimum {\x}=\alpha^2, then \alpha and \alpha^2 are the roots of the equation : [8 Apr 2024 Shift 2]

Correct Answer is : x2−6x+8=0

Application of Derivatives Part 3

Section: Mathematics

Question : 24 of 30

Marks: +1, -0

If the function f(x)=2x3−9ax2+12a2x+1,a>0 has a local maximum at x=α and a local minimum x=α2, then α and α2 are the roots of the equation :

[8 Apr 2024 Shift 2]

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