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12 December, 08:07

What are the zeros of the polynomial function? f (x) = x^4-4x^3-22x^2+4x+21

-3

-1

0

1

3

7

+2
Answers (1)
  1. 12 December, 08:28
    0
    Replace

    f

    (

    x

    )

    f

    (

    x

    )

    with

    y

    y

    .

    y

    =

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    y

    =

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    To find the roots of the equation, replace

    y

    y

    with

    0

    0

    and solve.

    0

    =

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    0

    =

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    Rewrite the equation as

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    =

    0

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    =

    0

    .

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    =

    0

    2

    x

    3

    -

    4

    x

    2

    -

    22

    x

    +

    44

    =

    0

    Factor the left side of the equation.

    Tap for more steps ...

    2

    (

    x

    -

    2

    )

    (

    x

    2

    -

    11

    )

    =

    0

    2

    (

    x

    -

    2

    )

    (

    x

    2

    -

    11

    )

    =

    0

    Divide both sides of the equation by

    2

    2

    . Dividing

    0

    0

    by any non-zero number is

    0

    0

    .

    (

    x

    -

    2

    )

    (

    x

    2

    -

    11

    )

    =

    0

    (

    x

    -

    2

    )

    (

    x

    2

    -

    11

    )

    =

    0

    Set

    x

    -

    2

    x

    -

    2

    equal to

    0

    0

    and solve for

    x

    x

    .

    Tap for more steps ...

    x

    =

    2

    x

    =

    2

    Set

    x

    2

    -

    11

    x

    2

    -

    11

    equal to

    0

    0

    and solve for

    x

    x

    .

    Tap for more steps ...

    x

    =



    11

    ,

    -



    11

    x

    =

    11

    ,

    -

    11

    The solution is the result of

    x

    -

    2

    =

    0

    x

    -

    2

    =

    0

    and

    x

    2

    -

    11

    =

    0

    x

    2

    -

    11

    =

    0

    .

    x

    =

    2

    ,



    11

    ,

    -



    11
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