Graph
A third degree polynomial with 2 zeros

For a third degree polynomial, we need 3 linear factors.

Since

5

and

2

i

are roots (zeros), we know that

x

−

5

and

x

−

2

i

are factors.

If we want a polynomial with real coeficients, then the complex conjugate of

2

i

(which is

−

2

i

) must also be a root and

x

+

2

i

must be a factor.

One polynomial with real coefficients that meets the requirements is

(

x

−

5

)

(

x

−

2

i

)

(

x

+

2

i

)

=

(

x

−

5

)

(

x

2

+

4

)

=

x

3

−

5

x

2

+

4

x

−

20

Any constant multiple of this also meets the requirements.

For example

7

(

x

3

−

5

x

2

+

4

x

−

20

)

=

7

x

3

−

35

x

2

+

28

x

−

140

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

any options?

step-by-step explanation: