COLUMN-I		COLUMN-II
a.	The non-repeated root of x3 + 4x2 + 5x + 2 = 0	p.	4
b.	If f(x) = x4 + 3x2 –6x –2 then the coefficent of  x3 in f(x+1) is	q.	33
c.	If $\mathrm{\alpha },\mathrm{\beta },\mathrm{\gamma }$ are the roots of x3 – x2 + 8x – 6 = 0 then  $(1+\mathrm{\alpha })(1+\mathrm{\beta })(1+\mathrm{\gamma })$ is	r.	16
d.	If one root of x3 – 12x2 + Kx – 18 = 0 is thrice the sum of remaining  two roots then k=	s.	-2

$\begin{array}{l}\mathrm{a}\to {\mathrm{f}}^1\left(\mathrm{x}\right)=3{\mathrm{x}}^2+8\mathrm{x}+5=0\\ \left(\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^3+4{\mathrm{x}}^2+5\mathrm{x}+2\right);\mathrm{x}=1\end{array}$
repeated root ‘–1’
$\begin{array}{l}\mathrm{\alpha }+\mathrm{\beta }+\mathrm{\gamma }=-4\\ -1-1+\mathrm{\gamma }=-4\Rightarrow \mathrm{\gamma }=-2\end{array}$
$\begin{array}{l}1\overline{)\begin{array}{l}103-6-2\\ 0114-2\end{array}}\\ 1\overline{)\begin{array}{l}11 4-2 \overline{)-4}\\ 011 4-2\end{array}}\\ \overline{)\begin{array}{l}12 6 \overline{)-4}\\ 013\end{array}}\\ \overline{)\begin{array}{l}13 \overline{)9}\\ 01 3\end{array}}\\ \overline{)4}\end{array}$
$x^4+4x^3+9x^2+4x-4=0$
C) $\alpha +\beta +\gamma =1,\alpha \beta +\beta \gamma +\beta \alpha =8,\alpha \beta \gamma =6$
$(1+\alpha )(1+\beta )(1+\gamma )=1+(\alpha +\beta +\gamma )+(\alpha \beta +\beta \gamma +\gamma \alpha )+\alpha \beta \gamma$$=1+1+8+6=16$
D) $\alpha =3(\beta +\gamma );\alpha +\beta +\gamma =12;4\alpha =12;\alpha =3$
$\begin{array}{l}\alpha =3\text{ is root of }{x}^3-12x^2+kx-18=0\\ k=33\end{array}$