If the roots of the equation x 3 − a x 2 + 14 x − 8 = 0 are all real and positive, then the minimum value of [ a ] (where [ a ] is the greatest integer of a ) is

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f ( x ) = x 3 − a x 2 + 14 x − 8 = 0 3 α + β + γ ​ 3 a ​ a ​ ≥ ( α ⋅ β ⋅ γ ) 1/3 ≥ ( 8 ) 1/3 ≥ 6 ​

Mathematics - Quadratic Equation Question with Solution | TestHub

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