The roots of the equation $x^2+kx+5 = 0$ differ by $\sqrt{61}$. Find the greatest possible value of $k$.
Question:
The roots of the equation $x^2+kx+5 = 0$ differ by $\sqrt{61}$. Find the greatest possible value of $k$.
Answer:
Let's think step by step.

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The roots of the equation $x^2+kx+5 = 0$ differ by $\sqrt{61}$. Find the greatest possible value of $k$.
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