Question

For each equation find all the roots


PLEASE HELP I AM SO CONFUSED

Answer 1

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

`x=(-1\pm√(1^2-4*1*1))/(2*1)} \\x=(-1 \pm√(1-4) )/(2) \\x=(-1 \pm√(-3))/(2) \\x=(-1\pm√(3) \iota)/(2)`

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