CPM Homework Help : A2C Problem 12-200

Use what you just proved about the sum and product of the roots of a quadratic equation, in problem 12-199, to write a quadratic equation for each of the following pairs of roots.

$- 3 + 5 i , - 3 - 5 i$
Hint (a):
$(-3 + 5i)+(-3-5i)=-\frac{b}{a}\rightarrow-6=-\frac{b}{a}$
$(-3+5i)(-3-5i)=\frac{c}{a}\rightarrow9-(-25)=\frac{c}{a}$
Example (a):
Choose a to be 1 and write the general quadratic equation using the values you find for b and c.
$x^{2} + 6x + 34 = 0$

$\frac { 1 } { 2 } \pm \frac { 3 } { 2 } i$
Hint (b):
See part (a).
Example (b):
$x^{2} − x + 1 = 0$

$7 \pm \sqrt { 3 }$
Hint (c):
See part (a).

$7, −6$
Hint (d):
See part (a).

$\frac { 2 } { 3 } , - \frac { 3 } { 4 }$
Hint (e):
See part (a).