Given quadratic equation:
![\[\mathbf{p}\text{ }+\text{ }\mathbf{7}\text{ }=\text{ }\mathbf{0},\text{ }\mathbf{q}\text{ }\text{ }\mathbf{12}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{px}\text{ }+\text{ }\mathbf{q}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bbfca56a64ea6b3e02d27242e420233f_l3.png "Rendered by QuickLaTeX.com")
So,
![\[p\text{ }=\text{ }-7\text{ }and\text{ }q\text{ }=\text{ }12\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ce2e55c4dae9870820b2e6e6e22c5b8e_l3.png "Rendered by QuickLaTeX.com")
Substituting the value of p and q in the given quadratic equation, we get
![\[\begin{array}{*{35}{l}} {{x}^{2}}~+\text{ }\left( -7 \right)x\text{ }+\text{ }12\text{ }=\text{ }0 \\ {{x}^{2}}~\text{ }7x\text{ }+\text{ }12\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3909526136ef683d1b7e100a7e09bd88_l3.png "Rendered by QuickLaTeX.com")
Solving for x by factorization, we have
![\[\begin{array}{*{35}{l}} {{x}^{2}}~\text{ }4x\text{ }\text{ }3x\text{ }+\text{ }12\text{ }=\text{ }0 \\ x\left( x\text{ }\text{ }4 \right)\text{ }\text{ }3\left( x\text{ }\text{ }4 \right)\text{ }=\text{ }0 \\ \left( x\text{ }\text{ }3 \right)\text{ }\left( x\text{ }\text{ }4 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-231e1ad60e795603494bff01d0f5a6a3_l3.png "Rendered by QuickLaTeX.com")
So,
![\[\begin{array}{*{35}{l}} x\text{ }\text{ }3\text{ }=\text{ }0\text{ }or\text{ }x\text{ }\text{ }4\text{ }=\text{ }0 \\ x\text{ }=\text{ }3\text{ }or\text{ }x\text{ }=\text{ }4 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ace7f308637b6798052bdbeb7e4c55e0_l3.png "Rendered by QuickLaTeX.com")
∴ Value of x =
![\[3,\text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3b2bc689dd0fabd8b36e9223949f4475_l3.png "Rendered by QuickLaTeX.com")
Find the values of x if
Given quadratic equation:
So,
Substituting the value of p and q in the given quadratic equation, we get
Solving for x by factorization, we have
So,
∴ Value of x =
