? 發問於 科學及數學數學 · 1 十年 前

f.4 maths

Let f(x) = 3x^3+mx^2-nx-7.When f(x) is divided by (x+1)(x-3),the remainder is 2x-4.

a)find the valuesf(-1) and f(3).

b)set up two equations connecting m and n.

c)Find the values of m and n.

1 個解答

評分
  • kwan
    Lv 6
    1 十年 前
    最佳解答

    a.

    ∵f(x)=3x^3+mx^2-nx-7

    f(x)=Q(x).(x+1)(x-3)+(2x-4)

    f(-1)=-6

    f(3)=2

    b.

    ∴3(-1)^3+m(-1)^2-n(-1)-7=-6

    -3+m+n=-6

    m+n=-3

    3(3)^3+m(3)^2-n(3)-7=2

    81+9m-3n-7=2

    3m-n=-24

    c.

    From b),

    m+n=-3------------------1

    3m-n=-24----------------2

    From 1), m=-3-n------3

    Sub 3 into 2, 3(-3-n)-n=-24

    -9-3n-n=-24

    -4n=-15

    n=15/4-------------------4

    Sub 4 into 1, m+15/4=-3

    m=-27/4

    2007-03-29 00:06:33 補充:

    Calculation mistakes= =b.∴3(-1)^3 m(-1)^2-n(-1)-7=-6-3 m n-7=-6m n=43(3)^3 m(3)^2-n(3)-7=281 9m-3n-7=23m-n=-24

    2007-03-29 00:06:46 補充:

    c.From b), m n=4-------------------13m-n=-24----------------2From 1), m=4-n------3Sub 3 into 2, 3(4-n)-n=-2412-3n-n=-24-4n=-36n=9-------------------4Sub 4 into 1, m 9=4m=-5

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