Find an nth-degree polynomial function with real coefficients satisfying the given conditions. Verify the real zeros and the given function value. n = 3, 2 and 2 - 3i are zeros, f(1) = -10

ddaeeric

ddaeeric

Answered question

2021-02-11

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. Verify the real zeros and the given function value. n = 3, 2 and 2 - 3i are zeros, f(1) = -10

Answer & Explanation

saiyansruleA

saiyansruleA

Skilled2021-02-12Added 110 answers

1) The coefficients of the polynomial are real numbers. Therefore, the complex zeros are conjugates of each other.
If 23i is a zero, then 2+3i is also a zero.
There are only three zeros: 23i,2+3i,2.
2) f(x)=k(x2)(x2+3i)(x23i), where k is a non-zero real number.
F(x)=k(x36x2+21x26)
Given that f(1)=10,
k(136×12+2126)=k(16+2126)=10k
k=1,f(x)=x36x2+21x26.
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