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



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.

Complex roots of quadratic equations (Answer

Part I

  1. 1/6 +/- √(11)/6 i
  2. -3/4 +/- √(31)/4 i

Part II

  1. x2 + 6x + 8
  2. x2 + 8x + 41

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