Question

Find a polynomial function that has the given zeros. (There are many correct answers.) −4, 6

Answer 1

If polynomial function vanishes at

x

=

a

, then

(

x

−

a

)

must be one of its factors.

Thus

(

x

−

7

)

,

(

x

−

4

−

√

6

)

and

(

x

−

4

+

√

6

)

are factors of the required polynomial.

The simplest polynomial that satisfies this is

(

x

−

7

)

(

x

−

4

−

√

6

)

(

x

−

4

+

√

6

)

=

(

x

−

7

)

{

(

x

−

4

)

−

√

6

}

{

(

x

−

4

)

+

√

6

}

=

(

x

−

7

)

{

(

x

−

4

)

2

−

6

}

=

(

x

−

7

)

(

x

2

−

8

x

+

16

−

6

)

=

(

x

−

7

)

(

x

2

−

8

x

+

10

)