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31 August, 13:51

If 5 + 6i is a root of the polynomial function f (x), which of the following must also be a root of f (x) ? - 5 - 6i 5 - 6i 6 - 5i 6 + 5i

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  1. 31 August, 14:02
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    Answer: 5-6i

    The rule is that if f (x) has real number coefficients, then a root of x = a+bi pairs up with its conjugate pair of x = a - bi. In this case, a = 5 and b = 6.
  2. 31 August, 14:13
    0
    5 - 6i is also the root of f (x).

    Step-by-step explanation:

    Given : If 5 + 6i is a root of the polynomial function f (x),

    To find : which of the following must also be a root of f (x).

    Solution : We have given that 5+6i is the on of the root of polynomial function f (x).

    It has two parts real and imaginary part so, it is a complex number.

    Real part = 5 and 6i is imaginary part.

    Complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of a + bi is a - bi.

    a = 5, b = 6.

    Then by the complex conjugate defination, Another root would be 5 - 6i

    Therefore, 5 - 6i is also the root of f (x).
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