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Write the discriminant of the following quadratic equations:
$\sqrt3 x^2 + 2\sqrt2 x - 2\sqrt3 = 0$
Given:
Given quadratic equation is $\sqrt3 x^2 + 2\sqrt2 x - 2\sqrt3 = 0$.
To do:
We have to find the discriminant of the given quadratic equation.
Solution:
Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,
$a=\sqrt3, b=2\sqrt2$ and $c=-2\sqrt3$.
The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.
Therefore,
$D=(2\sqrt2)^2-4(\sqrt3)(-2\sqrt3)=4(2)+8(3)=8+24=32$.
The discriminant of the given quadratic equation is $32$.
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