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March 26, 2017

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help me please im confused

Consider the quadratic expression X^2 + 4x + c = 0.

For what range of values does the equation have two complex roots?

what am i doing here can someone show me step by step so i can at least try to do the other problems i have

  • algebra - ,

    Hi. I answered you previous post and it was almost similar, except that here, the roots must be complex/imaginary so D must be less than zero. Anyway,

    Recall the formula for discriminant. For a quadratic equation in the general form, ax^2 + bx + c = 0,
    D = b^2 - 4ac
    if
    D = 0 : real, equal/double root
    D > 0 : two real, unequal roots
    D < 0 : two imaginary roots

    Since we're required to have complex/imaginary, D < 0, and solve for the unknown, c.
    x^2 + 4x + c = 0
    a = 1
    b = 4
    c = ?
    Substituting to the discriminant formula, (D < 0)
    0 < 4^2 - 4*1*c
    0 < 16 - 4c
    4c < 16
    c < 4

    Hope this helps~ :3

  • algebra - ,

    I disagree that the answer is c < 4. The correct answer is c > 4.

    Lets see the steps again:

    x^2 + 4x + c = 0, b^2 - 4ac < 0

    4^2 - 4(1)(c) < 0

    16 - 4c < 0

    16 < 4c

    4c > 16

    Therefore c > 4

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