If $\alpha$ and $\beta$ are the zeroes of $x^2 - 2x + 3$, find a polynomial whose zeroes are $\alpha + 2$ and $\beta + 2$.
Step-by-Step Solution
Key Concept: $\alpha + \beta = 2, \alpha \beta = 3$. New sum $= (\alpha + \beta) + 4 = 2 + 4 = 6$. New product $= (\alpha + 2)(\beta + 2) = \alpha \beta + 2(\alpha + \beta) + 4 = 3 + 4 + 4 = 11$.
New Sum $= 2 + 4 = 6$. [1.0 Mark]
New Product $= 3 + 2(2) + 4 = 11$. [1.0 Mark]
Polynomial is $x^2 - 6x + 11$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Calculating new sum $= 6$: 1.0 Mark
Calculating new product $= 11$: 1.0 Mark
Writing $x^2 - 6x + 11$: 1.0 Mark
Correct Answer: