Question

If $a\in R^{+}$ and the roots of the equation $a{x}^2-3x+c=0$ are two consecutive odd positive integers then?

• A. $a\in (0,\frac{3}{4}]$
• B. $a\in (1,\infty )$
• C. $a\in (1,4)$
• D. $a\in (0,\infty )$

Answer 1

The correct option is A $a\in (0,\frac{3}{4}]$

Let the roots be $\alpha$ and $\alpha +2$

$\Rightarrow$ $\alpha +\alpha +2=\frac{3}{a}$

$\Rightarrow$ $a=\frac{3}{2\alpha +2}$

smallest $\alpha =1$, largest $\alpha =\infty$

$\Rightarrow$ $a\in (0,3/4]$