Find the value of $k$
$3 k^{3} - 10 k^{2} + 9 k - 2 = 0$

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Solution

Given $3 k^{3} - 10 k^{2} + 9 k - 2 = 0 = p (x)$
when $k = 1$ $p (x) = 0$
Synthetic division
$(k - 1) (3 k^{2} - 7 k + 2)$
$(k - 1) (3 k^{2} - 6 k - k + 2)$
$(k - 1) [3 k (k - 2) - 1 (k - 2)]$
$(k - 1) (3 k - 1) (k - 2)$
$∴$ values of $k$ are
$k = \frac{1}{3}, 1, 2$

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