If alpha, beta, gamma are the roots of 2x^3 - | vedclass

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

Question

(B) Given the cubic equation $2x^3 + 0x^2 - 2x - 1 = 0$.Let the roots be $\alpha, \beta, \gamma$.According to Vieta's formulas for a cubic equation $a

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given the cubic equation $2x^3 + 0x^2 - 2x - 1 = 0$.Let the roots be $\alpha, \beta, \gamma$.According to Vieta's formulas for a cubic equation $ax^3 + bx^2 + cx + d = 0$,the sum of the roots taken two at a time is given by $\Sigma \alpha \beta = \frac{c}{a}$.Here,$a = 2$,$b = 0$,$c = -2$,and $d = -1$.Therefore,$\Sigma \alpha \beta = \frac{-2}{2} = -1$.We need to find $(\Sigma \alpha \beta)^2$.$(\Sigma \alpha \beta)^2 = (-1)^2 = 1$.

If $\alpha, \beta, \gamma$ are the roots of $2x^3 - 2x - 1 = 0$,then $(\Sigma \alpha \beta)^2$ is equal to

Similar Questions

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\,s$. In another $10\,s$ it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals

Data Entry - Physics

If $f: R \rightarrow R$ is defined by $f(x) = 7 + \cos(5x + 3)$ for $x \in R$,then the period of $f$ is

$A$ common emitter transistor amplifier has a current gain of $50$. If the load resistance is $4 \ k\Omega$ and input resistance is $500 \ \Omega$,the voltage gain of the amplifier is

Which of the following is a redox reaction?

Vedclass Test Series

Exam Paper Generator

Online Exam Module