Write the Discriminant of the Quadratic Equation √3x² + 2√2x − 2√3 = 0
Question
Write the discriminant of the following quadratic equation:
\[ \sqrt3x^2+2\sqrt2x-2\sqrt3=0 \]Solution
\[ a=\sqrt3,\quad b=2\sqrt2,\quad c=-2\sqrt3 \]
Using the formula,
\[ D=b^2-4ac \]
Substituting the values,
\[ D=(2\sqrt2)^2-4(\sqrt3)(-2\sqrt3) \]
\[ D=8+24 \]
\[ D=32 \]
Answer
\[
\boxed{D=32}
\]