Question 456027
write the quadratic equation that has these complex solutions:
{{{(3 +-i*sqrt(13))/2}}}
:
x = {{{(3 +-i*sqrt(13))/2}}}
:
multiply both sides by 2, get rid of the fraction
2x = {{{3 +-i*sqrt(13)}}}
:
Subtract 3 from both sides
2x - 3 = +/-{{{i*sqrt(13)}}}
;
Square both sides
(2x-3)^2 = i^2*13
:
Foil the left. i^2 = -1
4x^2 - 6x - 6x + 9 = -1 * 13
4x^2 - 12x + 9 = -13
4x^2 - 12x + 9 + 13 = 0
4x^2 - 12x + 22 = 0; is the equation
You can simplify, divide by 2
2x^2 - 6x + 11 = 0