I spent 1 day but can't solve, someone help pls!
a, B are the roots of X square + px +q =0 and a+3, B+3 are the roots of
X square + qx + p = 0
Find p and q ?
I know answer are 1 and -5
but I don't know how to prove it.
Maths problem
2011-10-27 5:01 am
回答 (1)
2011-10-27 5:28 am
✔ 最佳答案
a + b = - p.............(1)ab = q ..................(2)
a + b + 6 = - q .................(3)
(a + 3)(b + 3) = p .............(4)
From (4)
ab + 9 + 3(a + b) = p
From (2),(3) and (1),
q + 9 + 3(- 6 - q) = - (a + b) = - (- q - 6)
q + 9 - 18 - 3q = q + 6
3q = 9 - 18 - 6 = - 15, so q = - 5.
From (3) and (1),
- p + 6 = - q = 5
so p = 6 - 5 = 1.
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