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How is a quadratic inequality different from a quadratic equation?

  • Algebra - ,

    one is an inequality, the other is not. :-)

    An equation will have 0,1, or 2 roots.
    for example,

    (x-3)(x+4) = 0
    is true when x=3 or x = -4.

    (x-3)(x+4) < 0
    is the interval from -4 to 3, where y < 0.

    Just as the equation, the inequality may have an interval, or a point for a solution, or no solution at all.

    x^2 <= 0 has only x=0 for a solution.
    x^2 > 0 will have two intervals for a solution: (-oo,0) U (0,oo)
    x^2 < 0 has no real solutions at all

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