(C) Let $\alpha, \beta, \gamma$ be the roots of $x^3-3x^2+2x-1=0$. From the relation between roots and coefficients,the sum of the roots is $\alpha+\b

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(C) Let $\alpha, \beta, \gamma$ be the roots of $x^3-3x^2+2x-1=0$. From the relation between roots and coefficients,the sum of the roots is $\alpha+\beta+\gamma = -(-3)/1 = 3$. The roots of the new equation $x^3-x-1=0$ are $(\alpha-K), (\beta-K), (\gamma-K)$. For the equation $x^3+0x^2-x-1=0$,the sum of the roots is $0$. Therefore,$(\alpha-K)+(\beta-K)+(\gamma-K) = 0$. $(\alpha+\beta+\gamma) - 3K = 0$. Substituting the sum of the roots: $3 - 3K = 0$. $3K = 3$,which gives $K = 1$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Relation between roots and coefficients

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If the equation having the roots as the values obtained by diminishing each root of the equation $x^3-3x^2+2x-1=0$ by $K$ is $x^3-x-1=0$,then $K=$

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$2$
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$-1$
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$1$
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$-2$

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