Roots problem

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

Roots problem

Postby SArsalan on Fri May 10, 2013 3:30 pm

Hi
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.
SArsalan
 
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Re: Roots problem

Postby jg.allinsymbols on Fri May 10, 2013 5:37 pm

SArsalan wrote:Hi
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.
jg.allinsymbols
 
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