Question

The set of real values of $a$ for which the equation $x^2=a(x+a)$ has its root greater than $a$ is

• A. $(-2,-\frac{1}{2})$
• B. $(-\frac{1}{2},-\frac{1}{4})$
• C. $(-\infty ,0)$
• D. None of the above.

Answer 1

The correct option is D None of the above.

Given equation is $x^2-ax-a^2=0$

Roots are greater than a number $\Rightarrow$roots exists and there are real

$\Rightarrow a^2+4a^4>0$ which is always true

And f(a) >0

$\Rightarrow a^2-a^2-a^2>0$

$\Rightarrow -a^2>0$ which is always false

a belongs to null set in this case