Complex roots of quadratic equations

Complex roots of quadratic equations (Question)

Part I: Solve the following quadratic equation

1. 3x² – x + 1
2. 2x² + 3x + 5

Part II: Form the quadratic equation with the following roots

1. 3+i
2. 4-5i

Guide:

For a quadratic equation:
ax² + 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 +/- √(b²-4ac)/2a * i
x = p +/- qi

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

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