If ( x+2) and (x -1) are the factors of ( x3 + 10×2 + mx + n), then find the values of m and n. ​

Question

If ( x+2) and (x -1) are the factors of ( x3

+ 10×2

+ mx + n), then find the values of m and n.

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Alexandra 1 month 2021-08-12T18:00:22+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-12T18:01:44+00:00

    Answer:

    m=7, n= -18

    Step-by-step explanation:

    x+2=0

    x=-2

    p (x)=x^3+10x^2+mx+n

    p(-2)=-2^3+10×x^-2+m×-2+n

    p (-2)=-8+40-2m+n

    p (-2)=32-2m+n

    n=2m-32

    x-1=0

    x=1

    p (x)=x^3+10x^2+mx+n

    p (1)=1^3+10×1^2+m×1+n

    p (1)=1+10+m+n

    p (1)=11+m+n

    n= -m-11

    now,

    aad both answers

    n=2m-32

    n=-m-11

    put the subtraction sigh on second eq.

    n=2m-32

    -n=+m+11

    now,

    n=2m-32 -n=+m+11

    0=3m-21

    21=3m

    m=21÷3

    m=7

    n=-m-11

    n= -7-11

    n=-18

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