Polynomials
RD Sharma
CBSE
Grade 10
Question:
If $\alpha, \beta$ are zeroes of $p(x) = x^2 - k(x + 1) - c$, show that $(\alpha + 1)(\beta + 1) = 1 - c$.
Step-by-Step Solution
Key Concept: $p(x) = x^2 - kx - (k + c)$. $\alpha + \beta = k, \alpha \beta = -(k + c)$.
$(\alpha + 1)(\beta + 1) = \alpha \beta + \alpha + \beta + 1 = -(k + c) + k + 1 = 1 - c$. Proved! [3.0 Marks]
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🎯 Official CBSE Marking Scheme:
Expanding and substituting sum and product: 3.0 Marks
Correct Answer:
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