Question

Draw the graph of y = (x – 1)(x + 3) and hence solve x² – x – 6 = 0.

Answer 1

y = (x – 1)(x + 3) = x² – x + 3x – 3 = 0

y = x² + 2x – 3

Draw the parabola using the points (-4, 5), (-3, 0), (-2, -3), (-1,-4), (0, -3), (1, 0), (2, 5), (3, 12), (4, 21)

To solve the equation x² – x – 6 = 0, subtract x² – x – 6 = 0 from y = x² – 2x – 3.

Plotting the points (-2, -3), (-1, 0), (0, 3), (2, 9), we get a straight line.

The points of intersection of the parabola with the straight line gives the roots of the equation. The co-ordinates of the points of intersection forms the solution set.

∴ Solution {-2, 3}