SOLUTION: Show that neither x=1 nor x=-1 cxan be solution to the equations ax^2+2bx+a=0 where a and b are integers with b odd.

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Question 32201: Show that neither x=1 nor x=-1 cxan be solution to the equations ax^2+2bx+a=0 where a and b are integers with b odd.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
LET F(X)=AX^2+BX+A......NOT 2BX I THINK AS YOU CAN SEE BELOW....IF X=1 IS TO BE A SOLUTION THEN
F(1)=A+B+A=2A+B=0.....NOW B IS ODD...IT CANT B EQUAL TO -2A WHICH IS AN EVEN NUMBER.
SIMILARLY...F(-1)=A-B+A=2A-B=0.....NOW B IS ODD...IT CANT B EQUAL TO 2A WHICH IS AN EVEN NUMBER.
HENCE X=1 OR -1 BE THE SOLUTION...
YOU CAN SEE THAT THIS WILL NOT BE THE CASE IF IT IS 2B AND NOT B.