Root 2 x square 7 x 5 root 2

Asked by admin @ in Math viewed by 362 People

root 2 X square + 7 x + 5 root 2 is equal to zero solve the following quadratic equation and find the root by factorization

Answered by admin @


\textbf{Given:}

\sqrt{2}x^2+7x+5\sqrt{2}=0

\textbf{To find:}

\text{Roots of the given quadratic equation}

\textbf{Solution:}

\text{Consider,}

\sqrt{2}x^2+7x+5\sqrt{2}=0

\sqrt{2}x^2+2x+5x+5\sqrt{2}=0

\sqrt{2}x(x+\sqrt{2})+5(x+\sqrt{2})=0

(\sqrt{2}x+5)(x+\sqrt{2})=0

\sqrt{2}x+5=0\;\text{(or)}\;x+\sqrt{2}=0

\implies\,x=\dfrac{-5}{\sqrt{2}}\;\text{(or)}\;x=-\sqrt{2}

\therefore\textbf{Roots the required roots are $\bf\dfrac{-5}{\sqrt{2}},\,-\sqrt{2}$}


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