If $P, Q$ and $R$ are $3 imes 3$ matrices such that $\begin{aligned} & \left(\begin{array}{ccc} 3 x^2+x+3 & 2 x^2-x+4 & 7 x^2+8 x+5 \ 5 x^2+3 x+2 & 4 x^2-2 x-1 & 7 x^2+5 x+8 \ 3 x^2+2 x+5 & 4 x^2-x-2 & 3 x^2+8 x+7 \end{array} ight) \ & =P x^2+Q x+R, ext { then } \operatorname{det} R=…

Question

If $P, Q$ and $R$ are $3 	imes 3$ matrices such that $\begin{aligned} & \left(\begin{array}{ccc} 3 x^2+x+3 & 2 x^2-x+4 & 7 x^2+8 x+5 \ 5 x^2+3 x+2 & 4 x^2-2 x-1 & 7 x^2+5 x+8 \ 3 x^2+2 x+5 & 4 x^2-x-2 & 3 x^2+8 x+7 \end{array}ight) \ & =P x^2+Q x+R, 	ext { then } \operatorname{det} R= \end{aligned}$

Aicharya · Accepted Answer

Put $x=0$ in the given matrix $\left(\begin{array}{ccc} 3 & 4 & 5 \ 2 & -1 & 8 \ 5 & -2 & 7 \end{array}ight)=R$ $\Rightarrow R=3 	imes 9+4 	imes 26+5=136$

If $P, Q$ and $R$ are $3 \times 3$ matrices such that $\begin{aligned} & \left(\begin{array}{ccc} 3 x^2+x+3…

Solution