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Mathematics — CBSE Class 10 board question

Q1. [2]
If $\alpha$, $\beta$ are zeroes of the polynomial $p(x) = 5x^2 - 6x + 1$, then find the value of $\alpha + \beta + \alpha\beta$.
Previously asked in CBSE board exam
2024 30/5/1 Q23
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer

For $p(x) = 5x^2 - 6x + 1$, here $a = 5$, $b = -6$, $c = 1$.

Using the relationships between zeroes and coefficients:

$$\alpha + \beta = \frac{-b}{a} = \frac{-(-6)}{5} = \frac{6}{5}$$

$$\alpha\beta = \frac{c}{a} = \frac{1}{5}$$

Therefore:

$$\alpha + \beta + \alpha\beta = \frac{6}{5} + \frac{1}{5} = \frac{7}{5}$$

Source: Chapter 2, Section 2.3

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Explanation

The examiner awards marks for: (1) correctly identifying $a$, $b$, $c$ and applying the sum/product formulas, and (2) the final addition. Do not find individual zeroes — use the formulas directly. Writing the formulas before substituting shows method and earns step marks even if arithmetic slips.

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