Question

The values of $a$ for which the equation $2x^2-2(2a+1)x+a(a–1)=0$ has roots $\alpha \&\beta$ satisfying the condition $\alpha <a<\beta$, are

• A. $(-3,0)$
• B. $(0,\infty )$
• C. None of the above
• D. $(-\infty ,-3)\cup (0,\infty )$

Answer 1

The correct option is D

$(-\infty ,-3)\cup (0,\infty )$

Since, ‘a’ lies between the roots of the given equation

$\therefore f\left(a\right)<0$

Here, $f\left(x\right)=2x^2-2(2a+1)x+a(a-1)$

$\therefore f\left(a\right)=2a^2-2(2a+1)a+a(a-1)<0$

$\Rightarrow -a^2-3a<0\Rightarrow a(a+3)>0$

$\Rightarrow aϵ(-\infty ,-3)\cup (0,\infty )$