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Question
Graph the following quadratic equation and state their nature of solution
x2 + x + 7 = 0
Solution
Let y = x2 + x + 7
(i) Prepare the table of values for y = x2 + x + 7
| x | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |
| x2 | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 |
| x | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |
| 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |
| y | 19 | 13 | 9 | 7 | 7 | 9 | 13 | 19 | 27 |
(ii) Plot the points (– 4, 19) (– 3, 13) (– 2, 9) (– 1, 7) (0, 7) (1, 9), (2, 13) (3, 19) and (4, 27)
(iii) Join the points by a free hand smooth curve.
(iv) The solution of the given quadratic equation are the X-coordinates of the intersecting points of the parabola with the X-axis.
(v) The curve does not intersecting the X-axis. There is no solution set.
The equation x2 + x + 7 = 0 has no real roots.
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