I really need help with this. Can anyone help me please? Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
3,-2+2i

Thank you!

Step-by-step explanation:

A polynomial function is given by the form:

Where a is the leading coefficient, and p and q are the roots (more can be added if necessary).

Our zeros are 3 and (-2 + 2i).

And our leading coefficient a = 1.

Furthermore, by the Complex Root Theorem, if (-2 + 2i) is a zero, then (-2 - 2i) must also be a zero.

So, by substitution, we acquire:

Simplify:

Expand the second and third factors:

Therefore, our polynomial function of least degree and the given zeros will be:

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

f(x) = y

f(-3) = -5

step-by-step explanation: