1sky my Q is how are they saying a is odd
NOT " IF a IS odd "
[2]
1. if a and b are integers and x2 + ax + b =0 has discriminant as a perfect square then prove that its roots are integers.
SOLUTION IS :
roots are { - a± √ ( a2 -4b)} / 2
if a2 -4b = 4m , then a will be even and roots will be integers
if a2 -4b= (2m +1)22 , then a will be odd and then also the roots will be integers.
tell me by this how can they predict if a will be odd or even ?
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4 Answers
1a^2 -4b = 4m
=> a^2 = 4b +4m
now if a is odd....
a^2 is odd. so LHS is odd.
but RHS is even.