### Home > A2C > Chapter 12 > Lesson 12.5.1 > Problem12-200

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.

1. $- 3 + 5 i , - 3 - 5 i$

$(-3 + 5i)+(-3-5i)=-\frac{b}{a}\rightarrow-6=-\frac{b}{a}$

$(-3+5i)(-3-5i)=\frac{c}{a}\rightarrow9-(-25)=\frac{c}{a}$

Choose a to be 1 and write the general quadratic equation using the values you find for b and c.

$x^{2} + 6x + 34 = 0$

1. $\frac { 1 } { 2 } \pm \frac { 3 } { 2 } i$

See part (a).

$x^{2} − x + 1 = 0$

1. $7 \pm \sqrt { 3 }$

See part (a).

1. $7, −6$

See part (a).

1. $\frac { 2 } { 3 } , - \frac { 3 } { 4 }$

See part (a).