Question

If the equation $(a+1)x^2-(a+2)x+(a+3)=0$ has roots equal in magnitude but opposite in signs, then the roots of the equation are

• A. $\pm a$
• B. $\pm \frac{1}{2}a$
• C. $\pm \frac{3}{2}a$
• D. $\pm 2a$

Answer 1

Answer: (B)

Given equation is $(a+1)x^2-(a+2)x+(a+3)=0$
Since, roots are equal in magnitude and opposite in sign.
$\therefore$ coefficient of x is zero ie, $a+2=0$
$\Rightarrow$ $a=-2$ ..(i)
$\therefore$ Equation is $(-2+1)x^2-(-2+2)x+(-2+3)=0$
$\Rightarrow$ $-x^2+1=0$
$\Rightarrow$ $x=\pm 1$ ..(ii)
Only option [b] ie, $\pm \frac{1}{2}$
a satisfies Eqs. (i) and (ii).