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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [2] § 4.4 Nature of Roots § 4.5 Summary
Find the sum and product of the roots of the quadratic equation $2x^2 - 9x + 4 = 0$.
Previously asked in CBSE board exam
2023 30/4/1 Q23(A) (OR-1)
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer

For $2x^2 - 9x + 4 = 0$, we have $a = 2$, $b = -9$, $c = 4$.

$$\text{Sum of roots} = \frac{-b}{a} = \frac{-(-9)}{2} = \frac{9}{2}$$

$$\text{Product of roots} = \frac{c}{a} = \frac{4}{2} = 2$$

Source: Chapter 4, Quadratic Equations

Explanation

Examiners expect you to identify $a$, $b$, $c$ and directly apply the two formulae: sum $= -b/a$ and product $= c/a$. These follow from the quadratic formula — if $\alpha$ and $\beta$ are roots, then $\alpha + \beta = -b/a$ and $\alpha\beta = c/a$. No need to actually find the roots. Show the substitution step clearly for full marks.

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Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.