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Polynomials
RD Sharma
CBSE
Grade 10
Question:
If $\alpha, \beta$ are zeroes of $f(x) = a x^2 + b x + c$, form a quadratic polynomial whose zeroes are $\alpha + \dfrac{1}{\beta}$ and $\beta + \dfrac{1}{\alpha}$.
New Sum $= -\dfrac{b}{a} - \dfrac{b}{c} = -\dfrac{b(a + c)}{ac}$. [2.0 Marks] New Product $= \dfrac{c}{a} + 2 + \dfrac{a}{c} = \dfrac{c^2 + 2ac + a^2}{ac} = \dfrac{(a + c)^2}{ac}$. [2.0 Marks] Polynomial is $x^2 + \dfrac{b(a + c)}{ac} x + \dfrac{(a + c)^2}{ac}$ or $ac x^2 + b(a + c)x + (a + c)^2$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Evaluating new sum $= -b(a+c)/(ac)$: 2.0 Marks Evaluating new product $= (a+c)^2/(ac)$: 2.0 Marks Forming polynomial $ac x^2 + b(a+c)x + (a+c)^2$: 1.0 Mark
Correct Answer:
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