Question

Draw the graph of y = x² + x and hence solve x² + 1 = 0

Answer 1

Let y = x² + x

(i) Draw the graph of y = x² + x by preparing the table.

x	– 4	– 3	– 2	– 1	0	1	2	3	4
x2	16	9	4	1	0	1	4	9	16
y = x2 + x	12	6	2	0	0	2	6	12	20

(ii) Plot the points (– 4, 12), (– 3, 6), (– 2, 2), (– 1, 0), (0, 0), (1, 2), (2, 6), (3, 12) and (4, 20).

(iii) Join the points by a free hand to get smooth curve.

(iv) To solve x² + 1 = 0, subtract x² + 1 = 0 from x² + x we get.

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

The equation represent a straight line. Draw a line y = x – 1

x	– 3	– 1	0	2
y	– 4	– 2	– 1	1

Observe the graph of y = x² + 1 does not interset the parabola y = x² + x.

This x² + 1 has no real roots.