Determine the set of values of k for which the following  quadratic equations have real roots:
$2x^2+kx+2=0$

Given:

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

To do:

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

Solution:

$2x^2 + kx + 2 = 0$

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

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

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

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

$D=k^2-16$

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

Therefore,

$k^2-16≥0$

$k^2-(4)^2≥0$

$(k+4)(k-4)≥0$

$k≤-4$ or $k≥4$

The values of k are $k≤-4$ and $k≥4$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

53 Views

Kickstart Your Career

Get certified by completing the course

Get Started