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F.4 a maths 問題~!!! [ 10 分 ]

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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.

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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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