x^3+4x^2+x-6=0

Question

x^3+4x^2+x-6=0

Answer 1

Sum of the roots has to be = 4    Roots of ( a,b, c)   a + b + c = 4      a.b.c = -6

 

                                                      a = 3 , b= 2 , c = -1 will satisfy the equation

 

 

 The polynomial can be divided by either of the (x-3) ,(X -2) and ( x+1), resulting in a quadratic with 2 other roots.

       

 

 

Answer 2

Hi Maria,

 

x^3+4x^2+x-6=0

 

x^3-x^2+5x^2-5x+6x-6=0

x^2(x-1)+5x(x-1)+6(x-1)=0

(x^2+5x+6)(x-1)=0

(x^2 +3x+2x+6)(x-1)=0

{x(x+3)+2(x+3)}(x-1)=0

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

x+3=0 or x+2=0 or x-1=0

x=-3 ,  x=-2  ,   x=1

 

Ans: x= -3,-2 1.

 

 

Meena from Strongsville,Oh