Question

Find the possible values of m if the equation


`{x}^(2) - 4mx + 4m + 8 = 0`
has equal roots. solve the equation ??

Answer 1

For
`x^2-4mx+4m+8` to have one root, we need to have the discriminant be 0. Recall that for the general quadratic polynomial,


`ax^2+bx+c`


the discriminant is
`\Delta=b^2-4ac`. In this case,


`\Delta=(-4m)^2-4(4m+8)=16m^2-16m-32`

Solve for
`m` when
`\Delta=0`:


`16m^2-16m-32=0\implies m^2-m-2=0\implies (m-2)(m+1)=0`


`\implies m=2,m=-1`