MAH-CET 2026 — Mathematics PYQ

Step 1: Understand the standard form of a quadratic equation

The given equation is:

$$p{x}^2+qx+2=0$$

Comparing this with the general quadratic equation $a{x}^2+bx+c=0$, we identify the coefficients as:

• $a=p$

• $b=q$

• $c=2$

Step 2: Apply the condition for reciprocal roots

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

According to the question, the roots are reciprocal of each other. This means:

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

The formula for the product of roots in a quadratic equation is given by:

$$\text{Product of roots}=\alpha \cdot \beta =\frac{c}{a}$$

Substituting $\beta =\frac{1}{\alpha }$ into the product formula:

$$\alpha \cdot \left(\frac{1}{\alpha }\right)=\frac{c}{a}$$

$$1=\frac{c}{a}⟹a=c$$

Key Rule: For any quadratic equation, if the roots are reciprocal to each other, the coefficient of $x^2$ ($a$) must be equal to the constant term ($c$).

Step 3: Calculate the value of $p$

By substituting the values of our specific coefficients ($a=p$ and $c=2$) into the rule $a=c$:

$$p=2$$

Correct Answer

(d) $p=2$