Question

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

Answer 1

Let, f (x) =  k²x³ - kx² + 3kx - k

By factor theorem,  If (x - 3) is a factor of f(x) then f (3) = 0  :

⇒ k²(3)³ - k(3)² + 3k(3) - k = 0

⇒ k² × 27 - k × 9 + 9k - k = 0

⇒ 27k² – 9k + 9k – k = 0

⇒ 27k²  – k = 0

⇒k (27k – 1) = 0

⇒k = 0 or (27k – 1) = 0

k = 0 or k = 1/27

Hence, (x - 3) is a factor of f (x) when k = 0 or k = 1/27.

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Answer 2

$\frak \pink{solution}$

• g(x)=>x-3=0

=>x=3

Now,

f(x)=>k²x³ - kx² + 3kx - k=0

putting the value of x

=> k²(3)³ - k(3)² + 3k(3) - k = 0

=> k² × 27 - k × 9 + 9k - k = 0

=> 27k² – 9k + 9k – k = 0

=> 27k²  – k = 0

=>k (27k – 1) = 0

k = 0 or k = 1/27

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