Question

The equation $k^2{x}^2+kx+1=0$ has ____.

• A. equal roots
• B. two real roots
• C. real and distinct roots
• D. imaginary roots

Answer 1

The correct option is D imaginary roots

The given quadratic equation is $k^2{x}^2+kx+1=0$.
By comparing it with $a{x}^2+bx+c=0$, we get,
$a=k^2,b=k$ and $c=1$

$D=b^2-4ac$
$=(k{)}^2-4(k^2\left)\right(1)$
$=k^2-4k^2$
$=-3k^2$

$k^2$ will always be positive irrespective of the value of k.
Then, $-3k^2$ will be negative for any value of k.

Since the discriminant is less than zero, the equation has no real roots.