Polynomials
RD Sharma
CBSE
Grade 10
Question:
If $\alpha, \beta$ are zeroes of $p(x) = k x^2 + 4x + 4$ such that $\alpha^2 + \beta^2 = 24$, find $k$.
Step-by-Step Solution
Key Concept: $\alpha + \beta = -4/k, \alpha \beta = 4/k$. $\alpha^2 + \beta^2 = (-4/k)^2 - 2(4/k) = 16/k^2 - 8/k = 24$.
$16/k^2 - 8/k = 24 \Rightarrow 16 - 8k = 24k^2 \Rightarrow 3k^2 + k - 2 = 0$. [1.0 Mark]
$(3k - 2)(k + 1) = 0 \Rightarrow k = 2/3$ or $k = -1$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Forming quadratic $3k^2 + k - 2 = 0$: 1.0 Mark
Solving $k = 2/3$ or $k = -1$: 1.0 Mark
Correct Answer:
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