Question

1.Sa se descompună in factori ireductibili polinoamele:a)f=x la4-3x la 3+2x la2.
2.Sa se rezolve ecuatiile in C,stiind ca au solutiile indicate: a) x la3- 3x la2 +x+2=0, x1=2

Answer 1

1)f=$x^{4}-3 x^{3}+2x^2=x^2( x^{2} -3x+2)= x^{2} (x-2)(x-1)$
2)$x^{3}-3x^2+x+2=0,si, x_{1}=2,$. Scriem relati 1 si 3 a lui Vieta: 
$x_{1} + x_{2} + x_{3} =3,si, x_{1} x_{2} x_{3}=-2,$ inlocuind radacina data =2, obtinem sistemul: $x_{2} + x_{3}=1,si, x_{2} x_{3}=-1,$ care na dau ecuatia: x²-x-1=0, cu radacinile: [tex] x_{2}= \frac{1- \sqrt{5} }{2},si, x_{3}= \frac{1+ \sqrt{5} }{2} . [/tex]