2x-1 is a factor of 8x⁴+4x³-16x²+10x+m
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If 2x-1 is a factor of 8x⁴+4x³-16x²+10x+m
2x -1 =0
2x = 1
x = 1/2
Now put the value of x in given equation
8(1/2)⁴+ 4(1/2)³-16(1/2)²+10(1/2)+m=0
(1/2)+(1/2)-4+5+m=0
1+1-8+10+2m=0
4+2m=0
2m=-4
m=-2
2x -1 =0
2x = 1
x = 1/2
Now put the value of x in given equation
8(1/2)⁴+ 4(1/2)³-16(1/2)²+10(1/2)+m=0
(1/2)+(1/2)-4+5+m=0
1+1-8+10+2m=0
4+2m=0
2m=-4
m=-2
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