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

a: p(t) has degree 2 and zeros at t=−1 and t= 1 with y-intercept y= 4.


b: p(t) has degree 5 and zeros at t= 0, t= 2, and t=−4, with the multiplicity of t= 2 is 3.


c: p(t) has degree 3 and zeros at t= 3, t= 2i, and t=−2i.Make sure that p(t) in your final answer has real coefficients.


d: p(t) has degree 3 and zeros at t= 0 and t= 3−2i. Make sure that p(t) in your final answer has real coefficients.

Respuesta :

saraki

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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