1.If a and b are thr roots of thr quadratic equation 2x^2 + ax + b = 0,
where b ≠ 0 ,find the values of a and b.
F.4 a maths 問題~!!! [ 10 分 ]
2008-09-25 12:58 am
回答 (1)
2008-09-25 2:25 am
✔ 最佳答案
Since a and b are roots of equation.2a^2 + a^2 + b = 0
3a^2 + b = 0 ................(1) And
2b^2 + ab + b = 0
b(2b + a + 1) = 0
2b + a + 1 = 0 since b is not 0.
b = -( a + 1)/2. Sub into (1)
3a^2 - (a +1)/2 = 0
6a^2 - a - 1 = 0
a = [1 +/- sqrt(1 + 24)]/12 = [1 +/- 5]/12 = 1/2 and -1/3.
So b = -(1/2 + 1)/2 = -3/4 and -(-1/3 +1)/2 = -1/3.
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