The locus of the point P=(a, b) where a, b ar | vedclass

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Question

(c)

We have, $x^3+a x^2+b x+a=0$

Let $\alpha, \beta, \gamma$ are roots of equation and $\alpha, \beta, \gamma$ are in AP.

Put the values of $

Vedclass · Accepted Answer

a parabola whose vertex is on the $Y$-axis

Vedclass · Answer

(c)

We have, $x^3+a x^2+b x+a=0$

Let $\alpha, \beta, \gamma$ are roots of equation and $\alpha, \beta, \gamma$ are in AP.

Put the values of $\beta$ and $\alpha \gamma$ in Eq. (ii), we get

$\beta(\alpha+\gamma)+\gamma \alpha =b \Rightarrow 2 \beta^2+3=b$

$\Rightarrow 2\left(\frac{a^2}{9}ight)+3 =b \Rightarrow 2 a^2+27=9 b$

$\Rightarrow 2 a^2 =9 b-27$

$	herefore$ Locus of $P(a, b)$ is $2 x^2=9 y-27$ which represent the parabola whose vertex on $Y$-axis.

The locus of the point $P=(a, b)$ where $a, b$ are real numbers such that the roots of $x^3+a x^2+b x+a=0$ are in arithmetic progression is

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