JEE Main 2026 — 24 January, Evening Shift — Question 18

$x^{4}-a x^{2}+9=0$ let $\mathrm{x}^{2}=\mathrm{t}$

$\begin{gathered} \mathrm{t}^{2}-\mathrm{at}+9=0 \end{gathered}$ for roots of equation to be real & distinct roots of equation must be positive & distinct.

(i) $D>0 \Rightarrow a^{2}-36>0 \Rightarrow a \in(-\infty,-6) \cup(6, \infty)$

(ii) $\frac{-b}{2 a}>0 \Rightarrow \frac{a}{2}>0 \Rightarrow a>0$

(iii) $\mathrm{f}(0)>0 \Rightarrow 9>0 \Rightarrow \mathrm{a} \in \mathrm{R}$

By (i) $\cap$ (ii) $\cap$ (iii)

$\therefore \mathrm{a} \in(6, \infty)$

∴ least integral value of a is $7$