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Find the value of k, if \[\mathbf{3x}\text{ }\text{ }\mathbf{4}\] is a factor of expression \[\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}\text{ }\text{ }\mathbf{k}\].
Find the value of k, if \[\mathbf{3x}\text{ }\text{ }\mathbf{4}\] is a factor of expression \[\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}\text{ }\text{ }\mathbf{k}\].
Class 10 | Exercise 8A | ICSE | Maths | Remainder and Factor Theorems | Selina
Find the value of k, if \[\mathbf{3x}\text{ }\text{ }\mathbf{4}\] is a factor of expression \[\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}\text{ }\text{ }\mathbf{k}\].

Given, \[3x\text{ }\text{ }4\]is a factor of g(x) = \[\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}\text{ }\text{ }\mathbf{k}\].

So, \[f\left( 4/3 \right)\text{ }=\text{ }0\]

\[\begin{array}{*{35}{l}}

3{{\left( 4/3 \right)}^{2}}~+\text{ }2\left( 4/3 \right)\text{ }\text{ }k\text{ }=\text{ }0  \\

16/3\text{ }+\text{ }8/3\text{ }\text{ }k\text{ }=\text{ }0  \\

24/3\text{ }=\text{ }k  \\

k\text{ }=\text{ }8  \\

\end{array}\]

i

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