Question
Asked Oct 21, 2019
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Find a polynomial function f(x) having -1,2, and + i as zeros and f(3)=80

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Expert Answer

Step 1

Given information:

The function having zeros -1,2, and +i and f(3)80
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The function having zeros -1,2, and +i and f(3)80

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Step 2

Find the polynomial func...

The polynomial with real coefficients have complex roots occurring in
conjugate pair. For example, if one of the roots is a+ib, then must be
another root a -ib
Thus, the roots of the polynomial are -1,2,-i and +i
f(x) a(x-2)x1)(x-i)(x+ i)
= a(x-2)(x+1)(x2-2)
f(x) a(x-2)(x+1)(x2+1)
Since, f(3)80
f (3) a(3-2)(3+1)(3) +1)=80
80
1-4.10
a=2
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The polynomial with real coefficients have complex roots occurring in conjugate pair. For example, if one of the roots is a+ib, then must be another root a -ib Thus, the roots of the polynomial are -1,2,-i and +i f(x) a(x-2)x1)(x-i)(x+ i) = a(x-2)(x+1)(x2-2) f(x) a(x-2)(x+1)(x2+1) Since, f(3)80 f (3) a(3-2)(3+1)(3) +1)=80 80 1-4.10 a=2

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Math

Algebra

Polynomials