Question

determine the nature of the roots for the quadratic equation root 3 x square + 2 root 2 x minus 2 root 3 is equal to zero ​

Answer 1

$\textbf{Given:}$

$\textsf{Quadratic equation is}$

$\mathsf{\sqrt{3}x^2+2\sqrt{2}x-2\sqrt{3}=0}$

$\textbf{To find:}$

$\textsf{Nature of roots of the given quadratic equation}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{9cm} \\\textsf{The discriminant of the quadratic equation}\;\mathsf{ax^2+bx+c=0}\\\\\mathsf{is\;\;\triangle=b^2-4ac}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{\sqrt{3}x^2+2\sqrt{2}x-2\sqrt{3}=0}$

$\mathsf{a=\sqrt{3},\;b=2\sqrt{3},\;c=-2\sqrt{3}}$

$\mathsf{Now}$

$\mathsf{\triangle=b^2-4ac}$

$\mathsf{\triangle=(2\sqrt{3})^2-4{\times}\sqrt{3}{\times}(-2\sqrt{3})}$

$\mathsf{\triangle=12+24}$

$\mathsf{\triangle=36,\;a\;perfect\;square}$

$\therefore\textsf{The roots are real and rational}$

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Answer 2

medetermine the roots of quadratic equations root 3 x square + root 2 x minus 2 root 3 equals zero