Question

(3m+1)x²+2(m+1)x+m=0

Answer 1

(3m + 1)x2 + 2(m + 1)x + m = 0

Here a = 3m + 1, b = 2(m + 1), c = m

D = b2 - 4ac

= [2(m + 1)]2 - 4 x (3m + 1)(m)

= 4(m2 + 2m + 1) - 12m2 - 4m

= 4m2 + 8m + 4 - 12m2 - 4m

= -8m2 + 4m + 4

∴ Roots are equal.

∴ D = 0

⇒ -8m2 + 4m + 4 = 0

⇒ 2m2 - m - 1 = 0    ...(Dividing by 4)

⇒ 2m2 - 2m + m - 1 = 0

⇒ 2m(m - 1) + 1(m - 1) = 0

⇒ (m - 1)(2m + 1) = 0

Either m - 1 = 0,

then m = 1

or

2m + 1 = 0,

then 2m = -1

⇒ m = -1/2