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algebra 2

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what is the quadratic function that has the roots (4+3i) and (4-3i)

  • algebra 2 - ,

    there is a fast way to do this using the property
    if
    ax^2 + bx + c = 0, then
    sum or roots = -b/a
    product of roots = c/a

    sum of roots = (4+3i) + (4-3i) = 8
    product of roots = (4+3i)(4-3i) = 16-9 = 7

    equation:
    x^2 - 8x + 7 = 0

    another way is to form the factors:
    (x - (4+3i)) and (x - (4-3i)) and set

    (x - (4+3i))(x - (4-3i)) = 0
    (x - 4 - 3i)(x - 4 + 3i) = 0
    carefully expand, simplify and you will get the above answer.

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