Mathematics

Question

If you know a root of a function is -2 + the square root of 3i then _____. 2 + the square root of 3i is a possible root. 2 + the square root of 3i is a known root. -2 - the square root of 3i is a possible root. -2 - the square root of 3i is a known root. Just finished the assignment got it wrong but the correct answer is -2 - the square root of 3i is a known root

2 Answer

  • Answer:

    -2 - the square root of 3i is a known root

    Step-by-step explanation:

    we know that

    The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

    we have that

    The root of a function is [tex]-2+\sqrt{3}i[/tex]

    so

    Applying the conjugate root theorem

    [tex]-2-\sqrt{3}i[/tex] ---> is also a root of the function

    therefore

    -2 - the square root of 3i is a known root

  • Answer:

    -2 - Squared 3i is a known root

    Step-by-step explanation: