JEE Main · 2026 · 24 Jan 2026 · Shift 2 · Quadratic Equations and Inequalities

Put $t=x^2$, so the equation becomes $t^2-at+9=0$. Four real and distinct values of $x$ require two distinct positive roots in $t$. Their product is $9>0$ and their sum is $a$, so both roots are positive precisely when $a>0$; distinctness needs the discriminant $a^2-36>0$, i.e. $a>6$. The smallest positive integer satisfying $a>6$ is $7$.