Problema Solution
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. 1,-4 and 3+3 i are zeros. n=4 f(1)=-240
Answer provided by our tutors
If 3+3i is one of the zeros then so it 3-3i.
The equation can be written as:
f(x) = a(x - 1)(x - (-4))(x - (3 + 3i))(x - (3 - 3i))
f(x) = a(x^4 - 3x^3 - 4x^2 + 78x - 72)
click here to see the above simplification
f(x) = a(x^4 - 3x^3 - 4x^2 + 78x - 72)
Next we will find a by using f(1) = -240:
a(1^4 - 3*1^3 - 4*1^2 + 78*1 - 72) = -240
a*0 = -240
The equation a*0 = -240 has no solution thus there is no such n-the degree polynomial f(x) with zeros: 1,-4 3+3i and 3-3i and f(1) = -240.