1. The roots of the equation $4x^2 + 9x + 2 = 0$ are $-2$ and $-\frac{1}{4}$. Based on the root scaling property, what is the smaller root of the related equation $x^2 + 9x + 8 = 0$? ___
2. Let $r_1$ and $r_2$ be the roots of $5x^2 - 11x + 2 = 0$. Let $s_1$ and $s_2$ be the roots of $x^2 - 11x + 10 = 0$. What is the relationship between the roots?
3. The roots of $x^2 - 8x + 12 = 0$ are $2$ and $6$. For the related equation $2x^2 - 8x + 6 = 0$, what is the larger root? ___
4. If the roots of the quadratic equation $3x^2 + 10x - 8 = 0$ are $r_1$ and $r_2$, which of the following equations has the roots $3r_1$ and $3r_2$?
5. The roots of $x^2 - 5x - 6 = 0$ are $6$ and $-1$. The related equation $ax^2 - 5x + c = 0$ has roots that are $\frac{1}{2}$ times the roots of the first equation. What is the value of $c$? ___
6. What is the absolute difference between the roots of the quadratic equation $x^2 - 7x + 10 = 0$? ___
7. What is the absolute difference between the roots of the quadratic equation $3x^2 + 5x - 1 = 0$? ___
8. What is the absolute difference between the roots of the equation $-2x^2 + 6x - 1 = 0$?
9. For which of the following quadratic equations is the absolute difference between the roots equal to 0?
10. Calculate the absolute difference between the roots of the equation $4x^2 - 25 = 0$. ___