4.10 (1)x2 + mx - m = 0 D = m2 - 4(

4.10
2重解をもつので判別式 D = 0
(1)x2 + mx − m = 0
D = m2 − 4(−m)
m2 + 4m = 0 ⇔ m(m + 4) = 0
∴ m = 0, −4 のとき
(2)x2 + (m + 2)x + m2 = 0
D = (m + 2)2 − 4m2
− 3m2 + 4m + 4 = 0 ⇔ (3m + 2)(m − 2) = 0
∴ m = − 23 , 2 のとき
(3)x2 − 4mx + m + 3 = 0
D = 4m2 − (m + 3)
4m2 − m − 3 = 0 ⇔ (4m + 3)(m − 1) = 0
∴ m = − 43 , 1 のとき
(4)mx2 + 2(m − 1)x + (m + 1)
D = (m − 1)2 − m(m + 1)
∴m=
1
3
− 3m + 1 = 0 ⇔ m =
のとき
1
1
3