If $\alpha$ and $\beta$ are two zeroes of a polynomial $f(x) = px^2 - 2x + 3p$ and $\alpha + \beta = \alpha\b…

Question

If $\alpha$ and $\beta$ are two zeroes of a polynomial $f(x) = px^2 - 2x + 3p$ and $\alpha + \beta = \alpha\beta$, then value of $p$ is :

Accepted Answer

## Model Answer For $f(x) = px^2 - 2x + 3p$: $\alpha + \beta = \dfrac{2}{p}$ and $\alpha\beta = \dfrac{3p}{p} = 3$. Given $\alpha + \beta = \alpha\beta$: $\dfrac{2}{p} = 3 \Rightarrow p = \dfrac{2}{3}$. **Answer: (B) $\dfrac{2}{3}$** Source: Chapter 2, Section 2.3 ## Explanation Use the standard formulae: sum of zeroes $= -b/a$ and product of zeroes $= c/a$. Here $a=p,\ b=-2,\ c=3p$, giving sum $= 2/p$ and product $= 3$. Setting them equal solves directly for $p$. Students often make a sign error with $-b/a$ — note $b = -2$, so $-(-2)/p = 2/p$.

Mathematics — CBSE Class 10 board question