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प्रश्न
Draw the graph of y = 2x2 – 3x – 5 and hence solve 2x2 – 4x – 6 = 0
उत्तर
(i) Draw the graph of y = 2x2 – 3x – 5 by preparing the table of values given below.
| x | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |
| x2 | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 |
| 2x2 | 32 | 18 | 8 | 2 | 0 | 2 | 8 | 18 | 32 |
| – 3x | 12 | 9 | 6 | 3 | 0 | – 3 | – 6 | – 9 | – 12 |
| – 5 | – 5 | – 5 | – 5 | – 5 | – 5 | – 5 | – 5 | – 5 | – 5 |
| y | 39 | 22 | 9 | 0 | – 5 | – 6 | – 3 | 4 | 15 |
(ii) Plot the points (– 3, 22), (– 2, 9), (– 1, 0), (0, – 5), (1, – 6), (2, – 3), (3, 4), (4, 15) on the graph sheet using suitable scale.
(iii) To solve 2x2 – 4x – 6 = 0 subtract 2x2 – 4x – 6 = 0 from y = 2x2 – 3x – 5
y = 2x2 – 3x – 5
0 = 2x2 – 4x – 6
(–) (+) (+)
y = x + 1
(iv) y = x + 1 represent a straight line.
| x | – 4 | – 2 | 0 | 2 | 3 | 4 |
| y | – 3 | – 1 | 1 | 3 | 4 | 5 |
The straight line intersects the curve at (– 1, 0) and (3, 4).
From the two-point draw perpendicular lines to the X-axis it will intersect at – 1 and 3.
The solution set is (– 1, 3)
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