题目内容
考虑一元二次方程x2+mx+n=0,其中m、n的取值分别等于将一枚骰子连掷两次先后出现的点数,则方程有实根的概率为______.
连续抛掷两次骰子分别得到的点数记作(m,n):
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).共36个
若要使一元二次方程x2+mx+n=0有实根,则m2-4n≥0,则满足条件的情况有
(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(4,4),
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).共19种
故程有实根的概率P=
故答案为:36
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).共36个
若要使一元二次方程x2+mx+n=0有实根,则m2-4n≥0,则满足条件的情况有
(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(4,4),
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).共19种
故程有实根的概率P=
19 |
36 |
故答案为:36
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