Find the value of the discriminant.$\sqrt{2}x^2 + 4x +2\sqrt{2} = 0$.

Given :

The given equation is $\sqrt{2}x^2 + 4x +2\sqrt{2} = 0$.

To do :

We have to find the discriminant of the given equation.

Solution :

Discriminant of a quadratic equation $ax^2 + bx +c$ is given by,

$D = b^2 - 4ac$

In the given equation, $\sqrt{2}x^2 + 4x +2\sqrt{2} = 0$

$a = \sqrt{2}$, $b = 4$, $c = 2\sqrt{2}$.

$D = 4^2 - 4(\sqrt{2}) (2\sqrt{2})$

     $= 16 - 4 \times 2 \times 2 = 16 - 4 \times 4$

     $ = 16 -16 = 0$

Therefore, the discriminant of $\sqrt{2}x^2 + 4x +2\sqrt{2} = 0$ is 0.

$2\sqrt{2}$

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Updated on: 10-Oct-2022

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