Question

If $a$ and $b$ are the odd integers, then find nature of roots of the equation $2a{x}^2+(2a+b)x+b=0$, $a\ne 0$.

Answer 1

$\Rightarrow$ $2a{x}^2+(2a+b)x+b=0$

Here, $a=2a,b=2a+b,c=b$

$\Rightarrow$ Discriminant $=b^2-4ac$

$=(2a+b{)}^2-4(2a\left)\right(b)$

$=4a^2+b^2+4ab-8ab$

$=4a^2+b^2-4ab$

$=(2a-b{)}^2$

As discriminant is perfect square and $a$ and $b$ are integers, hence roots will be rational.