In the following, determine the set of values of k for which the given quadratic equation has real roots:
$3x^2 + 2x + k = 0$

Given:

Given quadratic equation is $3x^2 + 2x + k = 0$.

To do:

We have to find the values of k for which the roots are real.

Solution:

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

$a=3, b=2$ and $c=k$.

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

$D=(2)^2-4(3)(k)$

$D=4-12k$

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

Therefore,

$4-12k≥0$

$4≥12k$

$k≤\frac{4}{12}$

$k≤\frac{1}{3}$

Therefore, $k≤\frac{1}{3}$.

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Updated on: 10-Oct-2022

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