Question

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

• A. one real root
• B. two real roots
• C. no real roots
• D. equal roots

Answer 1

The correct option is C no real roots

Given quadratic equation: $k^2{x}^2+kx+1=0$

On comparing it with standard form $a{x}^2+bx+c=0$, we get

$a=k^2,b=k$ and $c=1$

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

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