Find the least positive value of k for which the equation $x^2 + kx + 4 = 0$ has real roots.

Given:

Given quadratic equation is $x^2 + kx + 4 = 0$.

To do:

We have to find the least positive value of k for which the given quadratic equation has real roots.

Solution:

$x^2 + kx + 4 = 0$

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

$a=1, b=k$ and $c=4$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.

$D=(k)^2-4(1)(4)$

$D=k^2-16$

The given quadratic equation has real roots if $D≥0$.

This implies,

$k^2-16≥0$

$k^2-(4)^2≥0$

$(k+4)(k-4)≥0$

$k≤4$ or $k≥4$

Therefore, the least positive value of $k$ is $4$.

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Updated on: 10-Oct-2022

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