Question

If the quadratic equation $a{x}^2+bx+b=0$ has the integer roots, where a and b are also intergers, then which of the following cannot be true

• A. $4a-b=0$
• B. $4a+b=0$
• C. $b=0$
• D. $b\ne 0$

Answer 1

The correct option is B $4a+b=0$

The roots are integers, so put the options and check if x is integer or not. on (i) $b=4a$ then $x^2+4x+4=0\Rightarrow x=-2$
(ii) $b=-4a$, then $x^2-4x-4=0\Rightarrow$ x is not integer.