Let alpha and beta be the two disinct roots o | vedclass

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

Question

Let ramining root is $\mathrm{r}$

then $\alpha \beta \gamma=1$ so $\alpha \beta=\frac{1}{\gamma}$

so req. eq. is $\frac{1}{x^{3}}+\frac{3}{x^{2}

Vedclass · Accepted Answer

$x^3 -3x -1 =0$

Vedclass · Answer

Let ramining root is $\mathrm{r}$

then $\alpha \beta \gamma=1$ so $\alpha \beta=\frac{1}{\gamma}$

so req. eq. is $\frac{1}{x^{3}}+\frac{3}{x^{2}}-1=0$

$=1+3 \mathrm{x}-\mathrm{x}^{3}=0$ $ \Rightarrow \boxed{{{	ext{x}}^3} - 3{	ext{x}} - 1 = 0}$

Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to

Similar Questions

The number of real solutions of the equation $\mathrm{x}|\mathrm{x}+5|+2|\mathrm{x}+7|-2=0$ is .....................

The two roots of an equation ${x^3} - 9{x^2} + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots will be

Let the sum of the maximum and the minimum values of the function $f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}$ be $\frac{m}{n}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$. Then $\mathrm{m}+\mathrm{n}$ is equal to :

Suppose the quadratic polynomial $p(x)=a x^2+b x+c$ has positive coefficient $a, b, c$ such that $b-a=c-b$. If $p(x)=0$ has integer roots $\alpha$ and $\beta$ then what could be the possible value of $\alpha+\beta+\alpha \beta$ if $0 \leq \alpha+\beta+\alpha \beta \leq 8$

If $\alpha, \beta$ are the roots of the equation, $x^2-x-1=0$ and $S_n=2023 \alpha^n+2024 \beta^n$, then