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Math Help - Need help in solving an inequality....

  1. #1
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    Need help in solving an inequality....

    Find the values of k for which the following equations have no roots.

    k^2 x^2 + 2kx + 1 = 0

    Using discriminant b^2 - 4ac, no roots would occur if it's < 0 .. So:

    (2k)^2 - 4(k^2) < 0
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by struck View Post
    Find the values of k for which the following equations have no roots.

    k^2 x^2 + 2kx + 1 = 0

    Using discriminant b^2 - 4ac, no roots would occur if it's < 0 .. So:

    (2k)^2 - 4(k^2) < 0
    (kx)^2 + 2kx + 1 = 0

    (kx + 1)^2 = 0

    (kx + 1) = 0

    kx  = -1

    x  = -1 /k

    When k = 0 , x has no values that can be called roots

    -------------------------------------

    If you are using quadratic formula for roots,

    Do you remember

    <br />
Roots ~are ~= \frac{-b \pm \sqrt{b^2-4ac}}{2a}

    What if a = 0 ??? Denominator is zero hence there are NO roots
    neither REAL nor COMPLEX
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