Question

Graph the following quadratic equation and state their nature of solution

x² – 9 = 0

Answer 1

Let y = x² – 9

(i) Prepare the table of values for y = x² – 9

x	– 4	– 3	– 2	– 1	0	1	2	3	4
x2	16	9	4	1	0	1	4	9	16
– 9	– 9	– 9	– 9	– 9	– 9	– 9	– 9	– 9	– 9
y	7	0	– 5	– 8	– 9	– 8	– 5	0	7

(ii) Plot the points (– 4, 7) (– 3, 0) (– 2, – 5) (– 1, – 8) (0, – 9) (1, – 8), (2, – 5) (3, 0) (4, 7)

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

(iv) The curve intersect the X-axis at – 3 and 3.
The solution is (– 3, 3).

(v) Since there are two points of intersection – 3 and 3 with the X-axis the quadratic equation has real and unequal roots.