Question

find the value of M so that 2 x minus 1 be a factor of 8 x power 4 + 4 x cube minus 16 X square + 10 X + m

Answer 1

let g(x)=2x-1
let g(x)=0
2x-1=0
2x=1
x=1/2.......(1)

let p(x)=8x^4+4x^3-16x^2+10x+m
let p(z)=0
8x^4+4x^3-16x^2+10x+m=0........(2)

put 'x' value in equation (2)
8(1/2)^4+4(1/2)^3-16(1/2)^2+10(1/2)+m=0
(8*1/16)+(4*1/8)-(16*1/4)+(10*1/2)+M=0
1/2+1/2-4+1/5+M=0
-28/10+M=0
M=28/10