If the Iines x + y = a and x – y = b touch the curve y = x2- 3x + 2 at the points where the curve intersects the x-axis then b/a is equal to

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

Solution:

The curve $y = x^{2} - 3 x + 2$ intersects $x -$ axis at $y = 0$ which gives $x = 1, x = 2 .$

So, the coordinates of points where $y = x^{2} - 3 x + 2$ crosses $x -$ axis are $(1, 0)$ and $(2, 0) .$

Lines $x + y = a$ and $x - y = b$ touch the curve $y = x^{2} - 3 x + 2$ at $(1, 0)$ and $(2, 0) .$

Therefore, $a = 1, b = 2 .$

Hence, $\frac{b}{a} = \frac{2}{1} = 2 .$

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