Question

if( X + 2 k) is a factor of f( x) is equals to X ki power 5 - 4 k Square x cube + 3 X + 2k + 3 , find k

Answer 1

let (x+2k) be q(x)
so,q(x)=0
x+2k=0
x={-2k},on putting x=-2k we get
f(-2k)=x^5-4k^2x^3+3x+2k+3
f(-2k)=(-2k)^5-4k^2(-2k)^3+3(-2k)+2k+3
f(-2k)=-32k^5+32k^5-6k+2k+3
f(-2k)=-4k+3
now,let -4k+3=0
so,-4k=-3
k=-3/-4
thus,k=3/4.