Quadratic Equations
RD Sharma
CBSE
Grade 10
Question:
If $\alpha$ and $\beta$ are roots of $x^2 - 5x + 6 = 0$, then the value of $\alpha^2 + \beta^2$ is:
(a) $13$
(b) $25$
(c) $12$
(d) $37$
Step-by-Step Solution
Key Concept: Roots are $2$ and $3$. $2^2 + 3^2 = 4 + 9 = 13$. Alternatively: $5^2 - 2(6) = 25 - 12 = 13$.
$\alpha + \beta = 5, \alpha \beta = 6 \Rightarrow \alpha^2 + \beta^2 = 5^2 - 2(6) = 25 - 12 = 13$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating $25 - 12 = 13$: 1.0 Mark
Correct Answer: $13$
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