Question

Graph the following quadratic equation and state their nature of solution

x² – 9x + 20 = 0

Answer 1

Let y = x² – 9x + 20

(i) Prepare the table of values for y = x² – 9x + 20

x	– 3	– 2	– 1	0	1	2	3	4	5	6
x2	9	4	1	0	1	4	9	16	25	36
– 9x	27	18	9	0	– 9	– 18	– 27	– 36	– 45	– 54
20	20	20	20	20	20	20	20	20	20	20
y	56	42	30	20	12	6	2	0	0	2

(ii) Plot the points (– 1, 30) (0, 20) (1, 12) (2, 6) (3, 2), (4, 0), (5, 0), (6, 2) ........(omit the high value)

(iii) Join the points by a free hand smooth curve.

(iv) The roots of the equation are the X-coordinates of the intersecting points of the curve with X-axis (4, 0) and (5, 0)

There are two points of intersection with the X-axis at 4 and 5. The solution set is 4 and 5.

The quadratic equation has real and unequal roots.

(v) Since there is two point of intersection with X-axis .......(different solution)

∴ The equation x² – 9x + 20 = 0 has real and unequal roots.