You know that the solutions of the general quadratic equation $ax^{2} + bx + c = 0$ are$x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$.

1. Find the sum $\frac { - b + \sqrt { b ^ { 2 } - 4 a c } } { 2 a } + \frac { - b - \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$.

   Answer (a):

   $-\frac{b}{a}$

2. Find the product $( \frac { - b + \sqrt { b ^ { 2 } - 4 a c } } { 2 a } ) ( \frac { - b - \sqrt { b ^ { 2 } - 4 a c } } { 2 a } )$.

   Answer (b):

   $\frac{c}{a}$

3. How is the sum of the solutions related to the original quadratic equation?

   Hint (c):

   What are a and b in the original equation?

4. How is the product of the solutions related to the original quadratic equation?

   Hint (d):

   What are a and c in the original equation?