MAH-CET 2026 — Mathematics PYQ

Step 1: Analyze the product of the roots

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

$$\alpha \cdot \beta =\frac{\text{Constant term}}{\text{Coefficient of }{x}^2}=\frac{c}{1}=c$$

We are given that c < 0. Since the product of the roots ($\alpha \cdot \beta$) is negative, the two roots must have opposite signs.

Given that \alpha < \beta, it follows that:

\alpha < 0 < \beta

Step 2: Analyze the sum of the roots

The sum of the roots is given by:

$$\alpha +\beta =\frac{-\text{Coefficient of }x}{\text{Coefficient of }{x}^2}=\frac{-b}{1}=-b$$

We are given that b > 0 (since 0 < b), which means -b < 0. Therefore, the sum of the roots is negative:

\alpha + \beta < 0

Step 3: Compare the magnitudes (absolute values) of the roots

Since $\alpha$ is negative and $\beta$ is positive, we can write $\alpha =-|\alpha |$. Substituting this into the sum inequality:

-|\alpha| + \beta < 0

\beta < |\alpha|

Combining this with our finding from Step 1 (\alpha < 0 < \beta), we get the complete relationship:

\alpha < 0 < \beta < |\alpha|

Correct Answer:

(b) \alpha < 0 < \beta < |\alpha|