sum and product of roots
2011-10-24 5:58 am
It is given that 3α+3β are the roots of the quadratic equation x^2+px+q=0.Form a quadratic equation in x whose roots are α+2β and β+2α , in terms of p and q
回答 (1)
2011-10-24 6:18 am
✔ 最佳答案
3α and 3β are the roots of x^2 + px + q = 03(α+β) = -p and 9αβ = q
So,
(α + 2β) + (β + 2α) = 3(α+β) = -p
(α + 2β)(β + 2α)
= 2(α^2 + β^2) + 5αβ
= 2(α+β)^2 + αβ
= 2p^2/9 + q/9
So, the quadratic equation in x whose roots are α+2β and β+2α is
x^2 + px + 2p^2/9 + q/9 = 0 or
9x^2 + 9px + (2p^2 + q) = 0
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https://hk.answers.yahoo.com/question/index?qid=20111023000051KK01027