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algebra

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Im lost i don't know how to do this can someone show me step by step how to solve this

For what value of c does the equation have one real root? Hint using the values of a and b found in the equation, solve D = 0 for c.

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

  • algebra -

    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 one real root, we equate D to zero, 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

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