# Need help in solving an inequality....

• Mar 24th 2009, 05:46 AM
struck
Need help in solving an inequality....
Find the values of k for which the following equations have no roots.

$\displaystyle k^2 x^2 + 2kx + 1 = 0$

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

$\displaystyle (2k)^2 - 4(k^2) < 0$
• Mar 24th 2009, 05:57 AM
Quote:

Originally Posted by struck
Find the values of k for which the following equations have no roots.

$\displaystyle k^2 x^2 + 2kx + 1 = 0$

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

$\displaystyle (2k)^2 - 4(k^2) < 0$

$\displaystyle (kx)^2 + 2kx + 1 = 0$

$\displaystyle (kx + 1)^2 = 0$

$\displaystyle (kx + 1) = 0$

$\displaystyle kx = -1$

$\displaystyle x = -1 /k$

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

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

If you are using quadratic formula for roots,

Do you remember

$\displaystyle Roots ~are ~= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

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