Show that this polynomial has three different real roots – math.stackexchange.com

Show that this polynomial has three different real roots – math.stackexchange.com

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There is polynomial $f(x)=x^3 +ax^2+bx+c$ and $ab=9c$ and $b<0$. Like in the title. I've only come up so far with $9x^3 + 9ax^2 + 9bx+ab=0$ and factoring here does nothing.

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