Question

A partial solution set is given for the polynomial equation. Find the complete solution set. (Enter your answers as a comma-separated list.)

x^4 − 2x^3 − 6x^2 + 14x − 7 = 0; {1, 1}

Answer 1

Hi,

Explanation:

Sol={-√7,1,1,√7}

`x^4-2x^3-6x^2+14x-7\\\\=x^4-x^3-x^3+x^2-7x^2+7x+7x-7\\\\=x^3(x-1)-x^2(x-1)-7x(x-1)+7(x-1)\\\\=(x-1)(x^3-x^2-7x+7)\\\\=(x-1)(x^2(x-1)-7(x-1))\\\\=(x-1)^2(x^2-7)\\\\\boxed{=(x-1)^2(x-√(7) )(x+√(7) )}\\`