Let R₁ and R₂ be the remainders when the polynomials $\mathrm{f}\left(\mathrm{x}\right)=4{\mathrm{x}}^3+3{\mathrm{x}}^2-12\mathrm{ax}-5$ and $\mathrm{g}\left(\mathrm{x}\right)=2{\mathrm{x}}^3+{\mathrm{ax}}^2-6\mathrm{x}+2$ are divided by x-1 and x+2 respectively. If $3{\mathrm{R}}_1+{\mathrm{R}}_2+28=0$, Then find the value of ‘a’

When  f(x) is divided by (x-1), the remainder = f(1) =R₁
When  g(x) is divided by (x+2), the remainder = g(-2) =R₂
$\begin{array}{l}{\mathrm{R}}_1=\mathrm{f}\left(1\right)=4+3-12\mathrm{a}-5=2-12\mathrm{a}\\ {\mathrm{R}}_2=\mathrm{g}(-2)=2(-2{)}^3+\mathrm{a}(-2{)}^2-6(-2)+2\\ =-16+4\mathrm{a}+12+2=4\mathrm{a}-2\\ \text{ If }3{\mathrm{R}}_1+{\mathrm{R}}_2+28=0\\ 3(2-12\mathrm{a})+4\mathrm{a}-2+28=0\\ 6-36\mathrm{a}+4\mathrm{a}+26=0\\ -32\mathrm{a}+32=0\\ 32\mathrm{a}=32; \mathrm{a}=1\end{array}$