Question

if aX square + bx + c and b x square plus a x + c have a common factor X + 1 then show that c=0 and a equals to b

Answer 1

Let f(x) be first polynomial
and g(x) be second.
They have common factors, x+1.
So f(-1)=0 and g(-1)=0
If we put -1 in x of f(x), we will get a-b+c=0----eq1
If we put -1 in x of g(x), we will get -a+b+c=0----eq2
If we solve eq1 and 2, we get 2c=0 so c=0
Put c=0 in eq1 or 2
Then we get a=b