If αandβ are the roots of the quadratic equation 2x^2+5x-4=0 ,find
the values of the following expressions.
(a)α^2-αβ+β^2
(b)2α^2+5αβ+2β^2
Quadratic equation １０
2009-10-12 6:05 am
回答 (1)
2009-10-12 6:16 am
✔ 最佳答案
2x^2 + 5x - 4 = 0Sum of roots = α + β = -5/2
Product of roots αβ = -4/2 = -2
(a)α^2 - αβ + β^2
= α^2 + 2αβ + β^2 - 3αβ
= (α + β)^2 - 3αβ
= 25/4 + 6
= 49/4
(b)2α^2 + 5αβ + 2β^2
= 2α^2 + 4αβ + 2β^2 + αβ
= 2(α^2 + 2αβ + β^2) + αβ
= 2(α + β)^2 + αβ
= 2(25/4) - 2
= 21/2
收錄日期: 2021-04-23 23:20:12
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