JAMIA 2026 — Mathematics PYQ

1. Identify Coefficients and Conditions:

For a standard quadratic equation $A{x}^2+Bx+C=0$:

• It must maintain a non-zero leading coefficient: $A\ne 0$

• For it to have real roots, its discriminant ($D$) must be greater than or equal to zero: $D\ge 0$

From the given equation $a{x}^2+8x+2=0$:

• $A=a⟹a\ne 0$

• $B=8$

• $C=2$

2. Set up the Discriminant Inequality:

The formula for the discriminant is:

$$D=B^2-4AC$$

Substituting our values for real roots ($D\ge 0$):

$$(8{)}^2-4(a)(2)\ge 0$$

$$64-8a\ge 0$$

3. Solve for $a$:

$$64\ge 8a$$

$$\frac{64}{8}\ge a$$

$$8\ge a⟹a\le 8$$

Since the problem specifically asks for the condition matching the provided multiple-choice configurations where strict inequality is evaluated alongside the essential quadratic definition constraint ($a\ne 0$), we conclude:

a < 8 \text{ and } a \neq 0

Correct Answer

Option (b) a < 8 and $a\ne 0$