I am facing a bit of a problem in understanding the following statement:
if c and d are the roots of (x-a)(x-b)+k=0, then a and b are the roots of (x-c)(x-d)=k
Now this is a true or false statement. I know its answer but can anyone please help in solving it.
The first statement is too vague, because we know nothing about c and d. We are only given the condition that c and d are roots of the given first equation.
The second equation is equivalent to (x-c)(c-d)-k=0. This this one, c and d are NOT roots. There is a formal way of showing the logic about all this, but it seems the entire description is false. False mostly because the conclusion is false.