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:

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

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- Mar 24th 2009, 05:46 AMstruckNeed 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 AMADARSH
$\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

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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