math

For what value of k does the equation x2 + kx + 9have:
Two distinct real roots
One real root
No real root

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asked by A
  1. One real root.

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  2. First of all you don't have an equation, you must have meant:
    x^2 + kx + 9 = 0

    For two distinct real roots, the discriminant b^2 - 4ac > 0
    k^2 - 4(1)(9) > 0
    k^2 > 36
    ±k > 6
    k > 6 or k < -6

    To have 1 root, the discriminant b^2 - 4ac must be zero
    k^2 - 4(1)(9) = 0
    k^2 = 36
    k = ± 6

    So what do you think must be the value of b^2 - 4ac to have no real roots ?

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    posted by Reiny
  3. 6 > k > -6 no roots?

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    posted by A
  4. yes, I would prefer you last statement to say

    -6 < k < 6

    I know it is the same thing as your answer, but traditionally let's go
    from left to right . Visualize the number line, negatives on the left.
    for -10 < x < 10 , I visualize x to be between -10 and + 10

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    posted by Reiny

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