For [tex]x^2-4mx+4m+8[/tex] to have one root, we need to have the discriminant be 0. Recall that for the general quadratic polynomial,
[tex]ax^2+bx+c[/tex]
the discriminant is [tex]\Delta=b^2-4ac[/tex]. In this case,
[tex]\Delta=(-4m)^2-4(4m+8)=16m^2-16m-32[/tex]
Solve for [tex]m[/tex] when [tex]\Delta=0[/tex]:
[tex]16m^2-16m-32=0\implies m^2-m-2=0\implies (m-2)(m+1)=0[/tex]
[tex]\implies m=2,m=-1[/tex]
