Q12. For what values of m, the equation (1+m)x2
+2(1+2m)x + 1+m =0 has equal roots.
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Answer:
for equal roots D=b
2
−4ac=0
⇒[2(m+1)]
2
−4m(3m+1)=0
⇒m
2
+2m+1−3m
2
−m=0
⇒−2m
2
+m+1=0
⇒2m
2
−m−1=0⇒(m−1)(m+
2
1
)=0
⇒
m=1,
2
−1
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