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Each of the roots of the equation $x^{3} - 6 x^{2} + 6 x - 5 = 0$ are increased by $K$ so that the new transformed equation does not contain $x^{2}$ term, then $K =$

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\frac{1}{3}

\frac{1}{2}

- 2

answer is D.

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Detailed Solution

The roots of equation

x^{3} - 6 x^{2} + 6 x - 5 = 0

each is increased by

k \Rightarrow α + k = x

$α = x - k$

$f (x) = k$

To eliminate the 2^nd $(x^{2})$ term.

Question Image

$3 k - 6 = 0$

$3 k = 6$

$k = \frac{6}{3} = 2$

$f (- k) = - 2$

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