(2x-3)(x+2)=0
2x² - 3x + 4x - 6 = 0
2x² + 1x-6 = 0
Let y = 2x² +X - 6= 0

Step 2:
The points to be plotted: (-4,22), (-3, 9), (-2, 0), (-1, -5), (0, -6), (1, -3), (2,4), (3,15), (4, 30)
Step 3:
Draw. the parabola and mark the co-ordinates of the intersecting point of the parabola with the x-axis.

Step 4:
The points of intersection of the parabola with the x-axis are (-2, 0) and (1.5,0).
Since the parabola intersects the x-axis at two points, the equation has real and unequal roots
∴ Solution {-2, 1.5}

x²-9=0
Let y=x²-9
Step 1:

Step 2:
The points to be plotted: (-4,7), (-3, 0), (-2, -5), (-1, -8), (0, -9), (1, -8), (2, -5), (3, 0), (4, 7)
(v) Real and equal roots
Step 3: 
Draw the parabola and mark the co-ordinates of the parabola which intersect the x-axis.

Step 4:
The roots of the equation are the co-ordinates of the intersecting points (-3, 0) and (3, 0) of the parabola with the x-axis which are -3 and 3 respectively.
Step 5:
Since there are two points of intersection with the x axis, the quadratic equation has real and unequal roots.
∴ Solution{-3, 3}

x² + x + 7 = 0
Let y=x2+x+7
Step 1:

Step 2:
Points to be plotted: (-4, 19), (-3, 13), (-2, 9), (-1, 7), (0, 7), (1, 9), (2, 13), (3, 19), (4, 27)
Step 3:
Draw the parabola and mark the co-ordinates of the parabola which intersect with the x-axis.

Step 4:
The roots of the equation are the points of intersection of the parabola with the x axis. Here the parabola does not intersect the x axis at any point.
So, we conclude that there is no real roots for the given quadratic equation.

x² - 8x + 16 = 0
Step 1 Prepare the table of values for the equation y = x² - 8x + 16

Step 2: Plot the points for the above ordered pairs (x, y) on the graph using suitable scale.

Step 3: Draw the parabola and mark the coordinates of the parabola which intersect with the X axis.
Step 4: The roots of the equation are the x coordinates of the intersecting points of the parabola with the X axis (4,0) which is 4.
Since there is only one point of intersection with X axis, the quadratic equation x² - 8x + 16 = 0 has real and equal roots.

x² - 9x + 20 = 0

Step 1:
Points to be plotted: (-4, 72), (-3,56), (-2,42), (-1, 30), (0, 20), (1, 12), (2, 6), (3, 2), (4, 0)
Step 2:
The point of intersection of the curve with x axis is (4, 0)
Step 3:

Since there is only one point of intersection with X axis, the quadratic equation x² + 9x + 20 = 0 has real and equal roots.
∴  Solution {4,4}