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gladu [14]
3 years ago
10

2. Find a polynomial function p(t) with integer coefficients that satisfy the given conditions.

Mathematics
1 answer:
anyanavicka [17]3 years ago
6 0

Step-by-step explanation:

Third-degree polynomial.

f(x) = a3 x3 + a2 x2 + a1 x + a0

Zeros at 4 and +/- 2i. That says you have factors that look like this:

(x - 4) (x2 + 4) <-- that second factor accommodates the complex zeros

And the constant coefficient of -128. So

f(x) = -128 (x - 4) (x2 + 4)

We'll multiply this through to find all the integer coefficients.

f(x) = -128 (x3 - 4x2 + 4x - 16)

a3 = -128

a2 = 512

a1 = -512

a0 = 2048

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