Find the value k if x-3 is a factor of k2 x3-k x2-3 k x-k

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Standard IX

Mathematics

Polynomials

Find the valu...

Question

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

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Solution

Let be the given polynomial.

By the factor theorem,

(x − 3) is a factor of f(x) if f (3) = 0

Therefore,

$\Rightarrow 27 k^{2} - 9 k + 9 k - k = 0 \Rightarrow 27 k^{2} - k = 0 \Rightarrow k (27 k - 1) = 0 \Rightarrow k = 0 o r k = \frac{1}{27}$

Hence, the value of k is 0 or .

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

Let be the given polynomial. By the factor theorem, (x − 3) is a factor of f(x) if f (3) = 0 Therefore, ⇒27k2-9k+9k-k=0⇒27k2-k=0⇒k27k-1=0⇒k=0 or k=127 Hence, the value of k is 0 or .

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

Let be the given polynomial.

By the factor theorem,

(x − 3) is a factor of f(x) if f (3) = 0

Therefore,

$\Rightarrow 27 k^{2} - 9 k + 9 k - k = 0 \Rightarrow 27 k^{2} - k = 0 \Rightarrow k (27 k - 1) = 0 \Rightarrow k = 0 o r k = \frac{1}{27}$

Hence, the value of k is 0 or .