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Question
Graph the following quadratic equation and state their nature of solution
x2 – 6x + 9 = 0
Solution
Let y = x2 – 6x + 9
(i) Prepare a table of values for y = x2 – 6x + 9
| x | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 | 5 |
| x2 | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 | 25 |
| – 6x | 24 | 18 | 12 | 6 | 0 | – 6 | – 12 | – 18 | – 24 | – 30 |
| 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
| y | 49 | 36 | 25 | 16 | 9 | 4 | 1 | 0 | 1 | 4 |
(ii) Plot the points (– 2, 25) (– 1, 16) (0, 9) (1, 4) (2, 1) (3, 0), (4, 1) and (5, 4) on the graph using suitable scale omit the points (– 4, 49) and (– 3, 36)
(iii) Join the points by a free hand smooth curve.
(iv) The X-coordinates of the point of intersection of the curve with X-axis are the roots of the, given equation, provided they intersect.
The solution is 3.
(v) Since there is only one point of intersection with X-axis the quadratic equation x2 – 6x + 9 = 0 has real and equal roots.
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