find values of k.

by hemangsarkar, Sep 10, 2012, 6:49 AM

Q) find the number of values of $k$ so that
$x^3 - 3x + k  = 0 $ has two distinct roots in $(5,10)$.

solution :

$f(x) = x^3 - 3x + k$

assume there are two real roots in $(5,10)$. then there must be at least one root of $f'(x)$ in the same interval.

$f'(x) = 3(x+1)(x-1)$ which has roots $1, -1$.

they don't lie in the desired interval.

hence no such value of $k$.

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    by boywholived, Sep 8, 2012, 12:02 PM

  • cool :lol:

    by subham1729, Sep 7, 2012, 6:44 AM

  • Awesome man !

    by Pheonix, Sep 6, 2012, 5:09 PM

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