value of p if x+1/2 is a factor of px raised to 2 - 4px + 3
 

We have,fx = px2 - 4px + 3Since, x + 12 is a factor of fx, then by factor theorem     f-12 = 0p-122 - 4p-12 + 3 = 0p4 + 2p + 3 = 0p + 8p + 124 = 09p = -12p = -129 = -43

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If x + 1/2 is a factor of the polynomial px2 - 4px + 3.
Then, x = -1/2.
  • p(x) = p(x)2 - 4px + 3
  • ​p(-1/2) = p(-1/2)2 - 4p(-1/2) + 3
  • p(-1/2) = p/4 + 2p + 3
  Now we know that since x + 1/2 is a factor of the polynomial .  
  • p/4 + 2p+ 3 = 0
  • p + 4(2p) + 4(3)/4  = 0
  • p + 8p + 12 = 0
  • 9p = -12
  • p = -12/9
  • p = -4/3.
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