Question

if the equation x^2 -(2+m)x +(m^2 -4m+4)=0 in x has equal roots ,find the value of m

Answer 1

Given = equal roots
so, D=0
b²-4ac=0
where a= 1 b= -(2+m) and c=m²-4m+4
putting the values
-(2+m)²-4(1)(m²-4m+4)=0
4+4m+m²-4m²+16m-16=0
-3m²+20m-12=0
multiple by (-)
so, 3m²-20m+12=0
spitting the middle term
3m²-18m-2m+12=0
3m(m-6)-2(m-6)=0
3m-2=0 or m-6=0
m=2/3 or m=6
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