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17 June, 18:49

Write the polynomial function of least degree that has zeros of x=-i and x=1

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  1. 17 June, 20:34
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    (x-1) (x^2 + 1)

    Step-by-step explanation:

    If the polynomial has two roots or zeros, then the least degree it can be is 2. But when x = - i is a root, generally x = i is a root too. Thus the degree here is 3. Using the roots, you can write the polynomial by finding a factor from each. The zeros are the solution to the factor. So if x = 1, it came from the factor x - 1. x = 1 is the solution because x - 1 = 0 is x = 1 solved.

    When x = - i, i this is the result of a square root of a negative number. So x had the exponent 2. To write the factor for x = - i, you should write x^2 + 1. When solved x = + / -√-1 = + / - i.

    The function is likely (x-1) (x^2 + 1).
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