Question

hallar 2 raices del polinomio x3- 7x + 6

Answer 1

x^3-6x-x+6=0
(x^3-x)-6(x-1)=0
x(x^2-1)-6(x-1)=0
x(x-1)(x+1)-6(x-1)=0
(x-1)[x(x+1)-6]=0
(x-1)(x^2+x-6)=0
x-1=0  =>  x=1
x^2+x-6=0   discr=1+24=25  
   x=(-1+5)/2=4/2=2
   x=(-1-5)/2=-6/2=-3

Answer 2

Sea P₍ₓ₎=x³-7x-6

 =x³-6x-x-6
 =x³-x-6x-6
 =x(x²-1)-6(x-1)
 =x(x+1)(x-1)-6(x-1)
 =(x-1)[x(x+1)-6]
 =(x-1)(x²+x-6)
 =(x-1)(x+3)(x-2)

⇒Raices P₍ₓ₎= (1,-3,2)