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  4. If the roots of cubic equation x3-6 x2+k x-8=0 are positive real numbers, then find the value of ( k -7)

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Q. If the roots of cubic equation $x^3-6 x^2+k x-8=0$ are positive real numbers, then find the value of $( k -7)$

Sequences and Series

Solution:

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Arithmetic mean of roots $=2$
Geometric mean of roots $=2$
$\Rightarrow \alpha=\beta=\gamma=2 $
$\text { So, } k=12 \Rightarrow k-7=5$