question_answer

Simplify : \[3x\left( 4x-5 \right)+3\]and find its value

(a) \[x=3\]

(b) \[x=\frac{1}{2}:\]

Answer:

\[3x\left( 4x-5 \right)+3~\]                       \[=3x\left( 4x-5 \right)+3~\]

\[=12{{x}^{2}}-15x+3\]

(a) For x=3,                   \[=12{{\left( 3 \right)}^{2}}-15\left( 3 \right)+3\]

\[=12\left( 9 \right)-45+3\]

\[=108-45+3=66\]

(b) For\[x=\frac{1}{2}\],                \[=12{{\left( \frac{1}{2} \right)}^{2}}-15\left( \frac{1}{2} \right)+3\]

\[=3-\frac{15}{2}+3\]

\[=6-\frac{15}{2}\]

\[=\frac{12-15}{2}=\frac{-3}{2}\]