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