Answer:
Given quadratic equation is, \[\sqrt{2}{{x}^{2}}+7x+5\sqrt{2}=0\] \[\sqrt{2}{{x}^{2}}+5x+2x+5\sqrt{2}=0\] [Splitting middle term] \[\Rightarrow \] \[x\left( \sqrt{2}x+5 \right)+\sqrt{2}\left( \sqrt{2}+5 \right)=0\] \[\Rightarrow \] \[\left( \sqrt{2}x+5 \right)\left( x+\sqrt{2} \right)=0\] \[\Rightarrow \] either \[\left( \sqrt{2}x+5 \right)=0\] or \[\left( x+\sqrt{2} \right)=0\] \[\Rightarrow \] \[x=-\frac{5}{\sqrt{2}}\] or \[x=-\sqrt{2}\] Hence roots are \[\frac{-5}{\sqrt{2}}\] and \[-\sqrt{2}\]
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