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Complex roots of quadratic equations

Question

Part I: Form the quadratic equation with the following roots

1. 3+2i
2. 5-4i

Part II: Solve the following quadratic equation

1. 2x2 – x + 3
2. 2x2 + x + 3

Part I

1. x2 + 6x + 5
2. x2 + 10x + 41

Part II

1. 1/4 +/- √(23)/4 i
2. -1/4 +/- √(23)/4 i
Note:

From a quadratic equation:
ay2 + by + c = 0

Sum of the roots = -b/a
Product of roots = c/a

If the solutions are not real number,

y = -b/2a +/- √(b2-4ac/2a * i
y = r +/- si

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

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