1.Given that x2-12x+k=0 has rootsa and 2a, find the value of a, then find the value of k.
2. Given that x2+kx+12=0 has roots a and 2a, find the value of a. then find the value of k.
Root-Coefficent Relationships(6)
2007-11-11 9:19 pm
回答 (1)
2007-11-11 9:29 pm
✔ 最佳答案
1. Sum of roots = a + 2a = 3a = 12a = 4
The two roots are 4 and 8.
Product of roots = 4*8 = 32 = k
Hence a = 4 and k = 32
2. Product of roots = 2a^2 = 12
a^2 = 6
a = sqrt 6 or -sqrt 6
When a = sqrt 6, sum of roots = 3a = -k
3sqrt 6 = -k
k = -3sqrt 6
When a = -sqrt 6, sum of roots = -3sqrt 6 = -k
k = 3 sqrt 6
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