Find the value of p if 2x-1 is a factor of 2x^3+px^2+11x+p+3
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P is - 7
p(x) = 2x³ +px² +11x +p+3
Given that (2x-1) is a factor.
2x-1 = 0
x = 1/2
As 2x-1 is a factor of p(x), we get,
p(1/2) = 2(1/2)³ +p(1/2)² +11(1/2) + p +3
= 2(1/8) +p(1/4) +11/2 +p +3
= 1/4 + p/4 +11/2 +p +3
= (1+ p+22 +4p +12) /4
= (35 +5p )/4
As 2x-1 is a factor, the remainder would be zero,
(35 +5p)/4 =0
35 +5p =0
5p =-35
p =-35/5 =-7
p = -7
Therefore, the value of p is -7.
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