Question

If the lines $x+y=a$ and $x-y=b$ touch the curve $y=x^{2}-3 x+2$ at the points where the curve intersects the $x$ -axis, then $\frac{a}{b}$ is equal to

Answer 1

$y=x^{2}-3 x+2$
At $x$ -axis $y=0=x^{2}-3 x+2$
$x =1,2$
$\frac{d y}{d x}=2 x-3$
$A (1,0) B (2,0)$
$\left(\frac{d y}{d x}\right)_{x=1}=-1$ and $\left(\frac{d y}{d x}\right)_{x=2}=1$
$\# x + y = a $
$\Rightarrow \frac{ dy }{ dx }=-1$ So $A (1,0)$ lies on it
$\Rightarrow 1+0=a \Rightarrow a=1$
$\# x - y = b $
$\Rightarrow \frac{ dy }{ dx }=1$ So $B (2,0)$ lies on it
$2-0=b $
$\Rightarrow b=2$
$\frac{a}{b}=0.50$