JAMIA 2026 — Mathematics PYQ

1. Understand the Condition:

Let the two roots of the quadratic equation be $\alpha$ and $\beta$.

According to the problem, one root is the reciprocal of the other:

$$\beta =\frac{1}{\alpha }⟹\alpha \cdot \beta =1$$

2. Product of Roots Property:

For a standard quadratic equation $a{x}^2+bx+c=0$, the product of the roots is given by:

$$\alpha \cdot \beta =\frac{c}{a}$$

From the given equation $k{x}^2-17x+8=0$:

• $a=k$

• $b=-17$

• $c=8$

3. Solve for $k$:

Equating the product of roots formula to $1$:

$$\frac{8}{k}=1$$

$$k=8$$

Key Rule to Remember: Whenever the roots of a quadratic equation are reciprocals of each other, the coefficient of $x^2$ is always equal to the constant term ($a=c$).

Correct Answer

Option (c) 8