Find the quadratic equation whose roots are [tex]3 \pm \frac{i}{2}[/tex].
Answer (2)
(x - root#1) times (x - root#2) = 0 . . . . . This is how to BUILD the quadratic equation.
All the rest is just multiplying out that first line:
(x- (3+i/2)) times (x - (3-i/2)) = 0
x² -x(3-i/2) -x(3+i/2) + (3+i/2)(3-i/2) = 0
x² -3x + ix/2 -3x - ix/2 + 9 -3i/2 + 3i/2 = 0
x² -6x +9 = 0 There it is. That's your quadratic equation.
The quadratic equation with roots 3 ± 2 i is 4 x 2 − 24 x + 37 = 0 . We determine this by using the factored form and applying properties of complex numbers. The process involves expanding and simplifying the roots into standard quadratic form.
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