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# Find the roots of the quadratic equations by applying the quadratic formula.

$2x^2 + x + 4 = 0$

Given:

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

To do:

We have to find the roots of the given quadratic equation.

Solution:

$2x^2 + x + 4 = 0$

The above equation is of the form $ax^2 + bx + c = 0$, where $a = 2, b = 1$ and $c = 4$

Discriminant $\mathrm{D} =b^{2}-4 a c$

$=(1)^{2}-4 \times 2 \times 4$

$=1-32$

$=-31$

$\mathrm{D}<0$

Therefore, real roots do not exist.

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