Respuesta :
we are given
solution of quadratic equation as
[tex] x=\frac{-3+-\sqrt{3}i}{2} [/tex]
we can also write it as
[tex] x=\frac{-3-\sqrt{3}i}{2} [/tex]
[tex] x=\frac{-3+\sqrt{3}i}{2} [/tex]
now, we can write it in terms of function
[tex] f(x)=(x-(\frac{-3+\sqrt{3}i}{2}))(x-(\frac{-3-\sqrt{3}i}{2})) [/tex]
Firstly , we can multiply it
[tex] =xx-\left(\frac{-3-\sqrt{3}i}{2}\right)x-\left(\frac{-3+\sqrt{3}i}{2}\right)x+\left(\frac{-3+\sqrt{3}i}{2}\right)\left(\frac{-3-\sqrt{3}i}{2}\right) [/tex]
[tex] x^2+3x+\frac{9}{4}-\frac{3i^2}{4}=0 [/tex]
now, we can simplify it
[tex] x^2+3x+\frac{9}{4}+\frac{3}{4}=0 [/tex]
[tex] x^2+3x+\frac{12}{4}=0 [/tex]
[tex] x^2+3x+3=0 [/tex]
so,
option-C.........Answer
