Question

$x^{4} - ax^{2} + 9 = 0$

let $x^{2} = t$

$$\begin{array}{r} t^{2} - at + 9 = \#(2) \end{array}$$

for roots of equation (1) to be real & distinct roots of equation (2) must be positive & distinct.

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

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

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

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

$$\therefore a \in (6,\infty) $$∴ least integral value of a is 7