Question

Example 2

Answer 1

Answer:

y=x-2

Step-by-step explanation:

If you have drawn the graph of $y = x^2 - 3x + 1$.

To determine the equation of the line which  should be drawn to solve the equation:  x² - 4x +3=0

Simply carry out the subtraction: $x^2 - 3x + 1 -(x^2 - 4x +3)$

$\implies x^2 -3x + 1-x^2 + 4x -3 \\= x^2 - x^2+ 4x - 3x-3 + 1\\=x-2$

The equation of the line which should be drawn is: y=x-2

What this means is simply:

If

$y = x^2 - 3x + 1 and y=x-2, then:\\x^2 - 3x + 1=x-2\\x^2 - 3x + 1-x+2=0\\x^2 - 4x + 3=0$