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```				   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
```

7 years ago

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```										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

```
7 years ago

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