PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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Let us discuss how to determine the nature of the solutions for the given quadratic equations.
Example:
1. Find the nature of the solution of the equation y = x^2 - 2x - 3.
 
Solution:
 
Step 1: Draw the graph of the equation y = x^2 - 2x - 3.
 
The table of values for the equation y = x^2 - 2x - 3 is:
 
x-2-101234
x^241014916
2x-4-202468
33333333
y50-3-4-305
 
Step 2: Plot the points in the graph using a suitable scale.
 
4.png
 
Step 3: Join the points by a smooth curve.
 
Step 4: In the graph, observe that the curve intersects the X - axis at 2 points (-1,0) and (3,0). Therefore, the roots of the equation are -1 and 3.
 
Since there are two points of intersection with the X - axis, the given equation has real and unequal roots.
 
 
2. Find the nature of the solutions of the equation y = x^2 - 10x + 25.
 
Solution:
 
Step 1: Draw the graph of the equation y = x^2 - 10x + 25.
 
The table of values for the equation y = x^2 - 10x + 25 is given by:
 
x34567
x^2916253649
10x3040506070
25
25
25
25
25
25
y41014
 
Step 2: Plot the points in the graph.
 
5 (2).png
 
Step 3: Join the points by a smooth curve.
 
Step 4: Here, the curve meets the X - axis at only one point. Therefore, the point of intersection of the parabola with X - axis for the given equation is (5,0).
 
Since the point of intersection is only one point with X - axis, the given quadratic equation has real and equal roots.