Question

Se considera x1,x2,x3 radacina polinomului f=x∧3-2x∧2+3x+m,unde m este nr reala)Calculati f(1)b)Aratati ca x1∧2+x2∧3+x3∧2=-2

Answer 1

$f(x)=x^3-2x^2+3x+m\Rightarrow f(1)=1-2+3+m=m+2$

Relatiile lui Viete:

$S_1=x_1+x_2+x_3=-\dfrac ba=2$
$S_2=x_1x_2+x_2x_3+x_3x_1=\dfrac ca=3$

$x_1^2+x_2^2+x_3^2=S_1^2-2S_2=4-6=-2$