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Find the value of k, if (x-3) is a facto...

Find the value of k, if `(x-3)` is a factor of `k^3x^3-x^2+3x-1`.

Text Solution

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Here, `f(x) = k^3x^3-x^2+3x-1`

As, `(x-3)` is a factor of `k^3x^3-x^2+3x-1`,
`:. f(3)` will be `0`.
`:. k^3(3)^3-(3)^2+3(3) - 1 = 0`
`=>27k^3 = 1`
`=> k = (1/27)^(1/3) = 1/3`
`=> k = 1/3`, is the required value of `k`.
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