Question

given a polynomial that has zeros of -2,4i, and -4i and has a value of 102 when x= -1. write the polynomial in standard form ax^n + bx^n-1 + …

Answer 1

To write the polynomial in standard form, determine the factors based on the given zeros. Use the complex conjugate to multiply the factors. Substitute the value of 'x' and polynomial value to find the coefficient 'a'. The polynomial in standard form is 51x^2 + 102x + 51.

Step-by-step explanation:

To write the polynomial in standard form, you need to determine the factors of the polynomial based on the given zeros. Since the polynomial has zeros of -2, 4i, and -4i, you know that the factors will be (x + 2), (x - 4i), and (x + 4i). Multiplying these factors using the complex conjugate, you get (x + 2)(x^2 + 16).

To find the value of 'a' in the standard form, substitute x = -1 and the value of the polynomial as 102. So, -3 * (-1 + 2)(-1^2 + 16) = 51. Therefore, the polynomial in standard form is 51x^2 + 102x + 51.

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