Madhya Pradesh Police Exam Model Paper 5

GIVEN:
${\mathit{x}}^2+\mathit{a}\mathit{x}+\mathit{b}$ ....(1)
${\mathit{x}}^2+\mathit{b}\mathit{x}+\mathit{a}$ ....(2)
CALCULATIONS:
From equation (1) , the equation is divided by x + 3 that means to solve this equation we have to put x = – 3 in the equation and the remainder is – 1 is taking the right side of the equation then,
${\mathit{x}}^2+\mathit{a}\mathit{x}+\mathit{b}$ ....(1)
$\Rightarrow 9-3\mathit{a}+\mathit{b}=-1\left(\because \mathit{x}=-3\right)$
$$$-3\mathit{a}+\mathit{b}=-10$.....(3)
Similarly for equation (2) , $\mathit{x}=3$
${\mathit{x}}^2+\mathit{b}\mathit{x}+\mathit{a}$ ....(2)
$\Rightarrow 9+3\mathit{b}+\mathit{a}=39$
$\Rightarrow \mathit{a}+3\mathit{b}=30$....(4) To find value of a and b solving equation (3) and (4) , by multiplying equation (4) with 3,
According to figure $10\mathit{b}=80\to \mathit{b}=8$
put b = 8 in equation (4) , $\mathit{a}+3\mathit{b}=30$
$\Rightarrow \mathit{a}+\left(3\times 8\right)=30$
$\Rightarrow \mathit{a}=6$
$\Rightarrow \mathit{a}+\mathit{b}=6+8=14$
$\therefore \mathit{a}+\mathit{b}=14$ .