Question

Find value of m so that be 2x-1be a factor of 8x⁴+4x³-16x²+10x+m.

Answer 1

Let f (x ) = 8x^4 + 4x^3 -16x^2 + 10x+m
. Hence using factor theorem. .
If 2x - 1 us factor of f (x) ,
then f (1/2) = 0
So.. f (1/2) = 8 (1/2)^4 + 4 (1/2)^3 - 16 (1/2)^2 + 10 (1/2) + m = 0
So, 1/2 + 1/2 - 4 + 5 + m = 0
So, 2 + m = 0
Hence m= -2