PUMPA - SMART LEARNING

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

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We have learnt that the roots of the quadratic equation ax^2 + bx + c = 0 can be found by the quadratic formula:
 
x=b±b24ac2a
 
Important!
b^2 - 4ac is called the discriminant of the quadratic equation ax^2 + bx + c = 0.
Let us discuss the nature of the roots of the quadratic equation depending on the discriminant.
 
Case I: b^2 - 4ac > 0
 
Here, b^2 - 4ac > 0. That means the value of the discriminant is positive.
 
Then, the possible roots are b+b24ac2a and bb24ac2a.
If b^2 - 4ac > 0, then the roots are real and distinct.
 
Case II: b^2 - 4ac = 0
 
Here, b^2 - 4ac = 0. That means the value of the discriminant is zero.
 
x=b+02a and x=b02a
 
x=b2a and x=b2a
 
The possible roots are b2a and b2a.
If b^2 - 4ac = 0, then the roots are real and equal.
 
Case III: b^2 - 4ac < 0
 
Here, b^2 - 4ac < 0. That means the value of the discriminant is negative.
 
We won't get any real roots in this case.
If b^2 - 4ac < 0, then there are no real roots.