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Q.

State true or false.


If x−2  is a factor of p x = x 3 −2x+3k  , then k= −4 3  .


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a

  True

b

  False 

answer is A.

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Detailed Solution

Given that, p  x  =  x 3 −2x + 3k  , and x – 2   is a factor of p  x  .
By factor theorem, if ( x - a) is a factor of f(x), then f(a) = 0.
Therefore, p  2  = 0  , i.e.,
⇒ 2 3 −2  2  + 3k = 0 ⇒8−4 + 3k = 0 ⇒4 + 3k = 0  
Calculating the value of k, we get,
  ⇒3k = − 4 ⇒k =  −4 3  
So, the value of k is -43.
Hence, the given statement is true and option 1 is correct.
 
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State true or false.If x−2  is a factor of p x = x 3 −2x+3k  , then k= −4 3  .