If alpha and beta are the roots of the equati | vedclass

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

Question

(D) Given the quadratic equation $x^2 + 2x + 4 = 0$.From the relation between roots and coefficients,we have $\alpha + \beta = -2$ and $\alpha \beta =

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(D) Given the quadratic equation $x^2 + 2x + 4 = 0$.From the relation between roots and coefficients,we have $\alpha + \beta = -2$ and $\alpha \beta = 4$.We need to find the value of $\frac{1}{\alpha^3} + \frac{1}{\beta^3} = \frac{\alpha^3 + \beta^3}{(\alpha \beta)^3}$.Using the identity $\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha \beta(\alpha + \beta)$:$\frac{1}{\alpha^3} + \frac{1}{\beta^3} = \frac{(\alpha + \beta)^3 - 3\alpha \beta(\alpha + \beta)}{(\alpha \beta)^3}$.Substituting the values $\alpha + \beta = -2$ and $\alpha \beta = 4$:$= \frac{(-2)^3 - 3(4)(-2)}{(4)^3} = \frac{-8 + 24}{64} = \frac{16}{64} = \frac{1}{4}$.

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + 2x + 4 = 0$,then $\frac{1}{\alpha^3} + \frac{1}{\beta^3}$ is equal to

Similar Questions

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-4x^2-9x+36=0$ such that $\alpha+\beta=0$,then $\alpha^2+2\beta^2+3\gamma^2=$

Consider the two equations $x^2 - 2ax + b^2 = 0$ and $x^2 - 2bx + a^2 = 0$. The arithmetic mean of the roots of the first equation is equal to what?

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+a x^2-b x+c=0$,then $\sum \beta^2(\gamma+\alpha) = $

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 + ax^2 + bx + c = 0$,then $\alpha^{-1} + \beta^{-1} + \gamma^{-1} = $

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - a(x + 1) - b = 0$,then $(\alpha + 1)(\beta + 1) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module