# Complex roots of quadratic equations

**Complex roots of quadratic equations (Question)**

Part I: Solve the following quadratic equation

- 3x
^{2}– x + 1 - 2x
^{2}+ 3x + 5

Part II: Form the quadratic equation with the following roots

- 3+i
- 4-5i

*Guide: *

For a quadratic equation:

ax^{2} + bx + c = 0

Sum of the roots = -b/a

Product of roots = c/a

For the case where the equation the solutions are not real number,

x = -b/2a +/- √(b^{2}-4ac)/2a * i

x = p +/- qi

Thus, the roots are p + qi and p – qi.

**Complex roots of quadratic equations (Answer**

Part I

- 1/6 +/- √(11)/6 i
- -3/4 +/- √(31)/4 i

Part II

- x
^{2}+ 6x + 8 - x
^{2}+ 8x + 41

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