Math: discriminant, hw help?

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  • 4 months ago
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    Think about the quadratic formula. The discriminant is that portion of the quadratic formula under the square root symbol, namely:

    d = b² - 4ac

    If the discriminant is negative (d < 0) then you are taking the square root of a negative and there will be 0 real roots.

    If the discriminant is zero (d = 0) then you are taking the square root of zero then the ± sign in front will give you the same solution (because ± 0 doesn't change anything).

    Finally, if the discriminant is positive (d > 0) then you have ± in front and you get two solutions.

    Summary:

    d = b² - 4ac

    d < 0 means 0 real solutions

    d = 0 means 1 real solution

    d > 0 means 2 real solutions

    In your particular quadratic:

    a = 3

    b = 24

    c = 48

    d = 24² - 4 * 3 * 48

    d = 0

    Answer:

    The discriminant is zero, so you have 1 real root.

    P.S. Please reread my reply in detail and let me know if there is *anything* I can clarify. Memorize the formula for the discriminant and then what it means.

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