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

one real root

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two real roots

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no real roots

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equal roots

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Solution

The correct option is C no real roots
Given quadratic equation: $k^{2} x^{2} + k x + 1 = 0$

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

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

$\Rightarrow$ Discriminant, $D = b^{2} - 4 a c$
$= (k)^{2} - 4 (k^{2}) (1)$
$= k^{2} - 4 k^{2}$
$= - 3 k^{2}$

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

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