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