Let us factorize the expression,
![\[\begin{array}{*{35}{l}} 2x{}^\text{2}\text{ }\text{ }9x\text{ }+\text{ }10\text{ }=\text{ }0 \\ 2{{x}^{2}}~\text{ }4x\text{ }\text{ }5x\text{ }+\text{ }10\text{ }=\text{ }0 \\ 2x\left( x\text{ }\text{ }2 \right)\text{ }\text{ }5\left( x\text{ }\text{ }2 \right)\text{ }=\text{ }0 \\ \left( 2x\text{ }\text{ }5 \right)\text{ }\left( x\text{ }\text{ }2 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3aa105cb172c2052663b79cc0b4d7f5a_l3.png "Rendered by QuickLaTeX.com")
So now,
![\[\begin{array}{*{35}{l}}</strong> <strong> \left( 2x\text{ }\text{ }5 \right)\text{ }=\text{ }0\text{ }or\text{ }\left( x\text{ }\text{ }2 \right)\text{ }=\text{ }0 \\</strong> <strong> 2x\text{ }=\text{ }5\text{ }or\text{ }x\text{ }=\text{ }2 \\</strong> <strong> x\text{ }=\text{ }5/2\text{ }or\text{ }x\text{ }=\text{ }2 \\</strong> <strong>\end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-68911a1547a5b0c788f77f09a4ced017_l3.png "Rendered by QuickLaTeX.com")
(i) When, x ∈ N then, x =
![\[2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b1e8e3db630df9050b1fec3c4066d5e6_l3.png "Rendered by QuickLaTeX.com")
(ii) When, x ∈ Q then, x =
![\[2,\text{ }5/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-302ebbccd4648ea5c17531cb333ba7f3_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{2x}{}^\text{2}\text{ }\text{ }\mathbf{9x}\text{ }+\text{ }\mathbf{10}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dbe33c788125bdfb3e1a84c26c5d3745_l3.png "Rendered by QuickLaTeX.com")
Let us factorize the expression,
So now,
(i) When, x ∈ N then, x =
(ii) When, x ∈ Q then, x =
