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If the root of the equation X square + bx + a b is equal to zero are real and equal then prove that the equation X square - 2 (a+b)x plus a square + b square + 2c squire=0 has no real root?

If the root of the equation X square + bx + a b is equal to zero are real and equal then prove that the equation X square - 2 (a+b)x plus a square + b square + 2c squire=0 has no real root?

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Aditya
 
From 1st equation
 
b² = 4ab 
Or
b = 4a or 0
 
Now
 
In second equation
Discriminant = 4(a+b)² - 4(a² +b² +2c²)
If b = 0
Then  it becomes
= 4 a² - 4a² -4b² - 8c² = -4b² -8c² 
Which is always negative hence no real roots.
 
Same condition with b = 4a
 
 
Regards
Arun (askIITians forum expert)

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