HCU MCA 2013 Paper

(b) Given that,f($\mathit{x}$) = $2{\mathit{x}}^3+\mathit{a}{\mathit{x}}^2+3\mathit{x}-5$
$\mathrm{and}$g($\mathit{x}$) = ${\mathit{x}}^3+{\mathit{x}}^2-4\mathit{x}-9$
also, f($\mathit{x}$), g($\mathit{x}$) give the same remainder when divided by $\mathit{x}+1$.
i.e.,zero of $\mathit{x}+1$
⇒$$ x+1 = 0
⇒$$x = - 1
∴$$f(-1) = g(-1)
$2{\left(-1\right)}^3+\mathit{a}{\left(-1\right)}^2+3\left(-1\right)-5={\left(-1\right)}^3+{\left(-1\right)}^2-4\left(-1\right)-9$
⇒$$- 2 + a - 3 - 5 = -1 + 1 + 4 - 9
⇒$$a - 10 = - 5
∴$$ a = 5