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

Comparing the given the quadratic equation with the standard form, we get
a = $k^2$, b = k, c = 1
We know that $D=b^2-4ac$
$\Rightarrow (k{)}^2-4(k^2\left)\right(1)$
$\Rightarrow k^2-4k^2$
$\Rightarrow -3k^2<0$
Regardless of the value of k, $-3k^2$ will be negative and since the discriminant is less than zero, the equation has no real roots.