Find the value of k if x -3 is a factor of k 2 x 3- kx 2-3 kx - k-

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Standard IX

Mathematics

Factor Theorem

Find the valu...

Question

Find the value of k if x-3 is a factor of k²x³-kx²+3kx-k.

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Solution

Equate the equation to zero.
hence,
k²x³-kx²+3kx-k=0
(x-3) is factor. That means, (x-3) = 0. Hence , x=3 must satisfy the equation. Substituting 3 instead of x in equation,

k^2 * 27 - k9 + 3k3 -k =0

27k^2 - 9k + 9k -k =0
27k^2 - k =0
27k^2 = k
27k = 1 ( cancel k on both sides)
k = 1/27.

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Find the value of k if x-3 is a factor of k2x3-kx2+3kx-k.

Equate the equation to zero. hence, k2x3-kx2+3kx-k=0 (x-3) is factor. That means, (x-3) = 0. Hence , x=3 must satisfy the equation. Substituting 3 instead of x in equation, k^2 * 27 - k*9 + 3k*3 -k =0 27k^2 - 9k + 9k -k =0 27k^2 - k =0 27k^2 = k 27k = 1 ( cancel k on both sides) k = 1/27.

Find the value of k if x-3 is a factor of k²x³-kx²+3kx-k.

Equate the equation to zero.
hence,
k²x³-kx²+3kx-k=0
(x-3) is factor. That means, (x-3) = 0. Hence , x=3 must satisfy the equation. Substituting 3 instead of x in equation,

k^2 * 27 - k9 + 3k3 -k =0

27k^2 - 9k + 9k -k =0
27k^2 - k =0
27k^2 = k
27k = 1 ( cancel k on both sides)
k = 1/27.