Question

Sa se formeze ecuatia de gradul al doilea cu coeficienti reali care admite solutia:
x$x_{1}$=$\frac{4-i}{2-3i}$

Answer 1

[tex]x_1= ^{2+3i)}\frac{4-i}{2-3i} = \frac{8-2i+12i-3i^2}{4-9i^2} = \frac{11+10i}{13} = \frac{11}{13} + \frac{10}{13} i\\ x_2=\frac{11}{13} - \frac{10}{13} i\\ S=x_1+x_2= \frac{22}{13} \\ P=x_1 \cdot x_2= \frac{221}{169}\\ x^2-Sx+P=0\\ x^2- \frac{22}{13} x+ \frac{221}{169}=0 [/tex]