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प्रश्न
Graph the following quadratic equation and state their nature of solution
(2x – 3) (x + 2) = 0
उत्तर
y = (2x – 3) (x + 2)
= 2x2 + 4x – 3x – 6
= 2x2 + x – 6
(i) Prepare a table of values for y from x – 4 to 4
| 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 |
| x | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |
| – 6 | – 6 | – 6 | – 6 | – 6 | – 6 | – 6 | – 6 | – 6 | – 6 |
| y | 22 | 9 | 0 | – 5 | – 6 | – 3 | 4 | 15 | 30 |
(ii) Plot the points (– 4, 22) (– 3, 9) (– 2, 0) (– 1, – 5) (0, – 6) (1, – 3), (2, 4), (3, 15) and (4, 30).
(iii) Join the points by a free hand smooth curve.
(iv) The curve intersect the X-axis at (– 2, 0) and `(1 1/2, 0)`
∴ The solution set is `(-2, 1 1/2)`
(v) Since there are two points of intersection with the X-axis, the quadratic equation has real and unequal roots.
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