Given: n=3. 4 and 2i are zeros. f(-1)=75 . Find an nth-degree polynomial function with real coefficients

Tabansi

Tabansi

Answered question

2021-09-09

n=3, 4 and 2i are zeros.
f(1)=75
Find an nth-degree polynomial function with real coefficients

Answer & Explanation

2abehn

2abehn

Skilled2021-09-10Added 88 answers

f(x)=a(x4)(x2i)(x+2i)
f(x)=a(x4)(x22ix+2ix+4)
f(x)=a(x4)(x2+4)
f(x)=a[x2(x4)+4(x4)]
f(x)=a(x34x2+4x16)
Use f(1)=75 to solve for a:
75=a[(1)34(1)2+4(1)16]
75=25a
a=3
f(x)=3x312x2+12x48

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