Question

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

Answer 1

Answer: 1

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