If the roots of the quadratic equation are α,β,obtain their sum and product using the formulas above.
1. x^2+(b/a)x+c/a=0
If the roots of x^2-4x+5=0 areα ,β,evaluate the following expressions.
1.(α-β)^2
2.α^2β+αβ^2
3. α^2+αβ+β^2
F4 A.maths Root-Coefficient2
2009-08-26 5:50 am
回答 (1)
2009-08-26 6:19 am
✔ 最佳答案
1. x2 + (b/a)x + c/a = 0Sum of roots α + β = -b/a
Product of roots αβ = c/a
If the roots of x2 – 4x + 5 = 0 are α ,β,evaluate the following expressions.
Sum of roots α + β = 4
Product of roots αβ = 5
1.(α – β)2
= α2 – 2αβ + β2
= α2 + 2αβ + β2 – 4αβ
= (α + β)2– 4αβ
= 16 – 20
= -4
2. α2β + αβ2
= αβ(α + β)
= (5)(4)
= 20
3. α2 + αβ + β2
= α2 + 2αβ + β2 – αβ
= (α + β)2 – αβ
= 16 – 5
= 11
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