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Question
Graph the following quadratic equation and state their nature of solution
x2 – 9 = 0
Solution
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.
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