find the value of k if 2x-1 is a factor of 2x3+ kx2+11x+k+5
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2x-1=0
2x=1
Therefore,x=1/2
Now,
or, 2x^3+Kx^2+11x+k+5=0
or, 2X(1/2)^3+KX(1/2)^2+11X(1/2)+k+5=0
or, 1/4+k/4+11/2+k+5=0
or, (1+k+22+4K+20)/4=0
or,5k+43=0
or, 5k=-43
Therefore, k= -43/5
2x=1
Therefore,x=1/2
Now,
or, 2x^3+Kx^2+11x+k+5=0
or, 2X(1/2)^3+KX(1/2)^2+11X(1/2)+k+5=0
or, 1/4+k/4+11/2+k+5=0
or, (1+k+22+4K+20)/4=0
or,5k+43=0
or, 5k=-43
Therefore, k= -43/5
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