If 1 is a multiple root of order 3 for the eq | vedclass

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(B) Given the equation $x^4-2x^3+2x-1=0$. Since $1$ is a root of order $3$,$(x-1)^3$ is a factor of the polynomial. We can write the polynomial as $(x

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$-1$

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(B) Given the equation $x^4-2x^3+2x-1=0$. Since $1$ is a root of order $3$,$(x-1)^3$ is a factor of the polynomial. We can write the polynomial as $(x-1)^3(x-k) = 0$,where $k$ is the fourth root. Expanding $(x-1)^3 = x^3-3x^2+3x-1$. Multiplying by $(x-k)$: $(x^3-3x^2+3x-1)(x-k) = x^4 - kx^3 - 3x^3 + 3kx^2 + 3x^2 - 3kx - x + k = 0$. $x^4 - (k+3)x^3 + (3k+3)x^2 - (3k+1)x + k = 0$. Comparing this with the original equation $x^4-2x^3+0x^2+2x-1=0$: From the constant term,$k = -1$. Therefore,the other root is $-1$.

If $1$ is a multiple root of order $3$ for the equation $x^4-2x^3+2x-1=0$,then the other root is

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