Answer:
Step-by-step explanation:
13.
x³-x²-x-2=0
x³-2x²+x^2-2x+x-2=0
x²(x-2)+x(x-2)+1(x-2)=0
(x-2)(x²+x+1)=0
x-2=0,x=2
x²+x+1=0
[tex]x=\frac{-1\pm\sqrt{1^2-4*1*1}}{2*1}} \\x=\frac{-1 \pm\sqrt{1-4} }{2} \\x=\frac{-1 \pm\sqrt{-3}}{2} \\x=\frac{-1\pm\sqrt{3} \iota}{2}[/tex]
12.
3x^4-11x³+15x²-9x+2=0
\[3x^4-3x^3-8x^3+8x²+7x²-7x-2x+2=0\]
3x³(x-1)-8x²(x-1)+7x(x-1)-2(x-1)=0
(x-1)[3x³-8x²+7x-2]=0
x-1=0,gives x=1
3x³-8x²+7x-2=0
3x³-3x²-5x²+5x+2x-2=0
3x²(x-1)-5x(x-1)+2(x-1)=0
(x-1)(3x²-5x+2)=0
x-1=0,gives x=1
3x²-5x+2=0
3x²-3x-2x+2=0
3x(x-1)-2(x-1)=0
(x-1)(3x-2)=0
x-1=0,gives x=1
3x-2=0, gives x=2/3
so roots are 2/3,1,1,1
