Question

If $a{x}^2+bx+c$ and $b{x}^2+ax+c$ have a common factor $x+1,$ hen prove that $c=0$ and $a=b$.

Answer 1

Consider the given polynomial.

$a{x}^2+bx+c$ …… (1)

$b{x}^2+ax+c$ …… (2)

x+1 is the factor of two polynomials means x = -1 satisfies two equation​s
$a-b+c=0$ …… (3)

$b-a+c=0$ …….. (4)

From equations (3) and (4), we get

$a=b$

$c=0$

Hence, proved.