Advertisements
Advertisements
प्रश्न
Graph the following quadratic equation and state their nature of solution
x2 – 6x + 9 = 0
उत्तर
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.
APPEARS IN
संबंधित प्रश्न
Graph the following quadratic equation and state their nature of solution
x2 – 9x + 20 = 0
Graph the following quadratic equation and state their nature of solution
x2 – 4x + 4 = 0
Graph the following quadratic equation and state their nature of solution
(2x – 3) (x + 2) = 0
Draw the graph of y = x2 – 4 and hence solve x2 – x – 12 = 0
Draw the graph of y = x2 + x and hence solve x2 + 1 = 0
Draw the graph of y = x2 + 3x + 2 and use it to solve x2 + 2x + 1 = 0
Draw the graph of y = 2x2 – 3x – 5 and hence solve 2x2 – 4x – 6 = 0
Draw the graph of y = (x – 1) (x + 3) and hence solve x2 – x – 6 = 0
The solution of (2x – 1)2 = 9 is equal to
Graph of a linear equation is a _______
