The cubic equation $x^3-10x^2+31x+q=0$ has roots $\alpha$, $\beta$ and $\gamma$ with \(\alph

Question

The cubic equation $x^3-10x^2+31x+q=0$ has roots $\alpha$, $\beta$ and $\gamma$ with $\alpha>\beta>\gamma$. Given that $\alpha=\beta+\gamma$ and $\alpha+1=\beta\cdot\gamma$. Find the value of $\alpha$. Show that $\beta=3$ and find the value of $\gamma$. Find the value of $q$.

Accepted Answer

$\alpha=5$, $\beta=3$, $\gamma=2$, $q=-30$.

IB Math HL January 2016 P1 Q5

IB Math HL January 2016 P1 Q5

Solution:

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