If 1/2
is a zero of the Polynomial P(x) 2x^3+ax^2+11x+a+3,find
the value of a.
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Answer:
p(x)= 2x^3+ax^2+11x+a+3
p(1/2)= 2×(1/2)^3+a×(1/2)^2+11×1/2+a+3
0 = 2×1/8+a×1/4+11/2+a+3
0 = 1/4+a/4+11/2+a+3= (1+a+22+4a+12)/4
0 = (5a+35)/4
5a+35= 0
5a= -35
a= -7
Therefore, the value of a in p(x)= 2x^3+ax^2+11x+a+3 is -7.
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