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No of integer values of b for which origin and (1,1) lie on same side of the line ax2+ bya+1=0 for every a belong to real numbers

No of integer values of b for which origin and (1,1) lie on same side of the line ax2+ bya+1=0 for every a belong to real numbers

Grade:11

1 Answers

Arun
25750 Points
5 years ago
b is in (2, ∞) 

Justification: 

i) The given line is: a²x + (ab)y + 1 = 0 

ii) Plugging (0,0), it is: 1; thus origin (0, 0) is above the line. 
So the point (1, 1) also has to be above the line; 
==> a² + ab + 1 > 0 

Taking this a quadratic in a, a is in R, if and only if its discriminant is ≥ 0 
==> b ≥ 2 [as b is given > 0, only positive value is considered and b ≤ -2 is rejected]

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