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

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

If the product of roots of the equation ${x^2} - 3kx + 2{e^{2\log k}} - 1 = 0$ is $7$, then its roots will real when

Suppose $m, n$ are positive integers such that $6^m+2^{m+n} \cdot 3^w+2^n=332$. The value of the expression $m^2+m n+n^2$ is

If $(x + 1)$ is a factor of ${x^4} - (p - 3){x^3} - (3p - 5){x^2}$ $ + (2p - 7)x + 6$, then $p = $

Suppose $a, b, c$ are three distinct real numbers, let $P(x)=\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+\frac{(x-a)(x-b)}{(c-a)(c-b)}$ When simplified, $P(x)$ becomes