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If λ and M be real numbers such that X 3 -λX 2 +mX-6=0 has its roots real and positive, then minimum value of M is

If λ and M be real numbers such that  X3-λX2+mX-6=0 has its roots real and positive, then minimum value of M is

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1 Answers

Pratham Ashish
17 Points
12 years ago

X3-λX2+mX-6=0

a+b + c  = λ

ab + bc + ca = m

abc = 6

applying A.M.   G.M. inequality,

(ab + bc + ca )/3 >=  ( ab.bc.ca) ^1/3

                        >  =  ( abc) ^2/3

                        > =    6^2/3

(ab + bc + ca )   >= 3 *  (6) ^2/3

 so its minimum value will be = 3 *  (6) ^2/3

  

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