1. Determine the range of k for which 3x2+8x+2k=0 has 2 different negative real solutions.
2. Given that x-2x-m+1=0 has 2 positive real number roots, α and β, determine the range of values of m.
Root-Coefficent Relationships(7)
2007-11-11 9:23 pm
回答 (1)
2007-11-11 9:34 pm
✔ 最佳答案
1. As there are 2 different real solutions,Discriminant = 8^2 - 4(3)(2k) > 0
64 - 24k > 0
24k < 64
k < 8/3
Also as both roots are negative, product of roots > 0
2k/3 > 0
k > 0
Hence the range of k is 0<k<8/3
2. Discriminant = (-2)^2 - 4(1)(1-m) > 0
4 - 4(1-m) > 0
1 - 1 + m > 0
m > 0
Product of roots = 1- m > 0
m < 1
The range of m is 0< m < 1
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