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If the sum of the zeroes of the quadratic polynomial $k x^{2}+2 x+3 k$ is equal to the product of its zeroes, then $\mathrm{k}=$ ? (a) $\frac{1}{3}$ (b) $\frac{-1}{3}$ (c) $\frac{2}{3}$ (d) $\frac{-2}{3}$
If the sum of the zeroes of the quadratic polynomial $k x^{2}+2 x+3 k$ is equal to the product of its zeroes, then $\mathrm{k}=$ ? (a) $\frac{1}{3}$ (b) $\frac{-1}{3}$ (c) $\frac{2}{3}$ (d) $\frac{-2}{3}$
CBSE | Class 10 | Excercise 2D | Maths | Polynomials | RS Aggarwal
If the sum of the zeroes of the quadratic polynomial $k x^{2}+2 x+3 k$ is equal to the product of its zeroes, then $\mathrm{k}=$ ? (a) $\frac{1}{3}$ (b) $\frac{-1}{3}$ (c) $\frac{2}{3}$ (d) $\frac{-2}{3}$

The correct option is option  (d) $\frac{-2}{3}$

$\alpha$ and $\beta$ be the zeroes of $\mathrm{kx}^{2}+2 \mathrm{x}+3 \mathrm{k}$.

Then $\alpha+\beta=\frac{-2}{k}$ and $\alpha \beta=3$

$\Rightarrow \alpha+\beta=\alpha \beta$

$\Rightarrow \frac{-2}{k}=3$

$\Rightarrow \mathrm{k}=\frac{-2}{3}$

i

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