# Complex roots of quadratic equations

**Question**

Part I: Form the quadratic equation with the following roots

- 3+2i
- 5-4i

Part II: Solve the following quadratic equation

- 2x
^{2}– x + 3 - 2x
^{2}+ x + 3

**Answer**

Part I

- x
^{2}+ 6x + 5 - x
^{2}+ 10x + 41

Part II

- 1/4 +/- √(23)/4 i
- -1/4 +/- √(23)/4 i

*Note:*

From a quadratic equation:

ay^{2} + by + c = 0

Sum of the roots = -b/a

Product of roots = c/a

If the solutions are not real number,

y = -b/2a +/- √(b^{2}-4ac/2a * i

y = r +/- si

Thus, the roots are r + si and r – si.

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