Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. Solve the two following problems.

Problem Number 1

n=4 ;
-1 , 4 , and 2+3i are zeros ;
f(1)= -120

f(x)= ?

Problem Number 2

n= 3 ;
-4 , and 7+4i are zeros ;
f(1)= 260

f(x)= ?

Thank you!

First function:f(x) = (20/11)*(x + 1) (x - 4) (x - 2 - 3i) (x - 2 + 3i)

Second function:f(x) = (x + 4) (x - 7 - 4i) (x - 7 + 4i)

Step-by-step explanation:

problem 1.)

nth degree : n = 4

roots   -1, 4, 2 + 3i  and 2 - 3i

f(1) = -120

f(x) = a*(x + 1) (x - 4) (x - 2 - 3i) (x - 2 + 3i)

f(1) = a* (1 + 1) (1 - 4) (1 - 2 - 3i) (1 - 2 + 3i) = -120

also

a*2*(-3)*(-1 - 3i) (-1 + 3i) = -120

a * -6 * ( 2 + 9) = -120

a *  -6 * 11 = -120

a = -120/-66 = 20/11

so f(x) = (20/11)*(x + 1) (x - 4) (x - 2 - 3i) (x - 2 + 3i)

n = 3

f(x) = a *(x + 4) (x - 7 - 4i) (x - 7 + 4i)

f(1) = a *(1 + 4) (1 - 7 - 4i) (1 - 7 + 4i) = 260

a * 5*( 36 + 16) = 260

a*5*52 = 260

a = 1

f(x) = (x + 4) (x - 7 - 4i) (x - 7 + 4i)

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step-by-step explanation: