A curve has equation $$\(y=\mathrm{f}(x)\)$$ where $$\(\mathrm{f}(x)=x^{4}-5 x^{3}+6 x^{2}+5 x-15\)$$. As shown in the diagram, the curve crosses the $$\(x\)$$-axis at the points $$\(A\)$$ and $$\(B\)$$ with coordinates $$\((a, 0)\)$$ and $$\((b, 0)\)$$ respectively. By first finding the quotient when $$\(\mathrm{f}(x)\)$$ is divided by $$\((x-3)\)$$, show that $$\[ a=-\sqrt{\frac{5}{2-a}} . \]$$ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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