sum and product of roots
2011-10-22 7:55 am
α,β are the roots of the quadratic equation x^2+px+q=0 and α+3,β+3 are the roots of the equation x^2+qx+p=0.Find the values of p and q.
回答 (1)
2011-10-22 8:16 am
✔ 最佳答案
α + β = -p, αβ = qα + β + 6 = -q, (α + 3)(β + 3) = p
So, -p + 6 = -q => q - p = -6
αβ + 3(α + β) + 9 = p
q + 3(-q - 6) + 9 = q + 6
-2q - 9 = q + 6
3q = -15
q = -5 and then p =1
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https://hk.answers.yahoo.com/question/index?qid=20111021000051KK00959