In the following, determine the set of values of k for which the given quadratic equation has real roots:
$2x^2 - 5x - = 0$

Given:

Given quadratic equation is $2x^2 - 5x - k = 0$.

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,

$a=2, b=-5$ and $c=-k$.

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

$D=(-5)^2-4(2)(-k)$

$D=25+8k$

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

Therefore,

$25+8k≥0$

$8k≥-25$

$k≥\frac{-25}{8}$

Therefore, $k≥\frac{-25}{8}$.

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Updated on: 10-Oct-2022

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