Question

Find a polynomial with integer coefficients that satisfies the given conditions.U has degree 5, zeros 1, 2, −2, and −i, and leading coefficient 4; the zero −2 has multiplicity 2.U(x) =

Answer 1

Answer:

Explanation:

Here, we want to write the polynomial that satisfies the given properties

Firstly, it is of degree 5:

It means that the highest power is 5

Now, let us look at the zeros:

x = 1: this means : x-1 is a root

x = 2 (of multiplicity 2)

This means

(x-2)(x-2)

x = -2

This means (x+2)

x = -i

i is the root of -1

x = -i

(x+i) = 0

Thus, we have the polynomial as follows;

$4(x-1)(x-2)(x-2)(x^2+1)$

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