Draw the graph of y = x² + 2x – 3 and hence find the roots of x² – x – 6 = 0.

We are given y = x² + 2x – 3

So taking the values of X in between –3 and 3 we can find various value of y and put them in graph

Again we are given

x² – x – 6 = 0

we can write the above expression as

x² + (2x–2x)–x –3–3 = 0

⇒ x² + 2x–3–2x–x–3 = 0

⇒ y–3x–3 = 0 (as x² – x – 6 = 0 )

⇒ y = 3x + 3

Now we can draw another pair of value using the above data

Now we can draw the graph and the intersection of the two lines will give the roots for the equation.

So the lines intersects at {–2,3} and (3,12).