Question

The equation $(a+2)x^2+(a-3)x=2a-1,a\ne -2$ has rational roots for

• A. all rational values of $a$ except $a=-2$
• B. all real values of $a$ except $a=-2$
• C. rational values of $a>\frac{1}{2}$
• D. none of these

Answer 1

The correct option is A all rational values of $a$ except $a=-2$

Roots of this equation
$x=\frac{-(a-3)\pm \sqrt{(a-3{)}^2+4(a+2\left)\right(2a-1)}}{2(a+2)}$
For rational number denominator should be not zero.
$a\ne -2$
Hence, option 'A' is correct.