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Find the nth-degree polynomial function with real coefficients satisfying the given conditions:
n=4; -3; 1/4, 2i are zeroes and f(-2)=-144.
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A polynomial of the degree 4 with real coefficients and the roots -3, , 2i is
f(x) = = . (1)
where "a" is the real number, a leading coefficient.
To find the value of "a", use the condition f(-2) = -144.
Substitute x= -2 into the polynomial (1). You will get
f(-2) = = = -288a.
Thus -288a = -144. Hence, a = = 0.5.
Finally, the polynomial is
f(x) = .