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Solve x^2 -3x is greater than or equal to 10

Would the solutions be x=5 and x= -2?

  • Algebra -

    no, you forgot about the inequality condition.

    You must have had
    (x-5)(x+2) ≤ 0

    here is a neat way to finish it
    draw a line and mark the "critical values" of -2 and +5
    this splits the line into 3 segments
    1. x < -2
    2. x between -2 and 5
    3. x > 5

    pick any x you want in each of the segments to test . You don't actually have to find the value just the +/- situation

    1. let x = -10 , so (-)(-) > 0 , NO
    2. let x = 0 , so (-)(+) < 0 YEs
    3. let x = 10, then (+)(+) > 0, NO

    so every value of x between -2 and 5 inclusive will work..
    -2 ≤ x ≤ 5 , x any real number

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