Question

If both the roots of the equation $x^2-9x+a=0$ are positive and one is greater than $3$ and other is less than $3$, then all possible values of $a$ is

• A. $0$ $<$ $a$ $<$ $18$
• B. $-1$ $<$ $a$ $<$ $2$
• C. $-18$ $<$ $a$ $<$ $0$
• D. None of the above.

Answer 1

The correct option is A $0$ $<$ $a$ $<$ $18$

From the diagram it is clear that $f(-3)<0$ and $f0)>0$

$9-27+a<0\Rightarrow a<18$

And $f\left(0\right)>0\Rightarrow a>0$

$\therefore 0<a<18$