Question

raizes da equação 3x³-7x²+8x-2=0

Answer 1

3x³-7x²+8x-2=0

3x³-7x²+2x +6x-2=0

3x³-7x²+8x +2(3x-1)=0

x*(3x²-7x+2) +2(3x-1)=0

####sabemos que P(x)=ax²+bx+c =a*(x-x')*(x-x'')  ..x' e x'' são as raízes

####3x²-7x+2 =3*(x-1/3)*(x-2)

x*(3*(x-1/3)*(x-2)) +2(3x-1)=0

x*((3x-1)*(x-2)) +2(3x-1)=0

(3x-1)*[x*(x-2)+2]=0

(3x-1)*(x²-2x+2)=0

3x-1=0 ==> x=1/3

x²-2x+2=0

x'=[2+√(4-8)]/2=(2+2I)/2=1+i

x''=[2-√(4-8)]/2=(2-2I)/2=1-i

Resposta ==> { 1/3 ; 1+i ; 1-i}