Let α and β be two disinct roots of equation x^3 + 3x^2 -1 = 0. equation which has (α β ) as&nbs

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4-2.Quadratic Equations and Inequations

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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

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

$x^3 -3x^2 + 1 = 0$

$x^3 + x^2 -3x + 1 = 0$

$x^3 + x^2 + 3x -1 = 0$

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{{{\text{x}}^3} – 3{\text{x}} – 1 = 0}$

Standard 11

Mathematics

normal

(KVPY-2020)

easy

normal

(KVPY-2016)

hard

(IIT-1982)

normal

(KVPY-2009)