If alpha, beta, gamma are the roots of the eq | vedclass

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

Question

(D) Given that $\alpha, \beta, \gamma$ are roots of $2x^3-5x^2+4x-3=0$. By Vieta's formulas: $\alpha+\beta+\gamma = \frac{5}{2}$,$\alpha\beta+\beta\ga

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(D) Given that $\alpha, \beta, \gamma$ are roots of $2x^3-5x^2+4x-3=0$. By Vieta's formulas: $\alpha+\beta+\gamma = \frac{5}{2}$,$\alpha\beta+\beta\gamma+\gamma\alpha = 2$,and $\alpha\beta\gamma = \frac{3}{2}$. We know that $\sum \alpha\beta(\alpha+\beta) = (\alpha+\beta+\gamma)(\alpha\beta+\beta\gamma+\gamma\alpha) - 3\alpha\beta\gamma$. Substituting the values: $\sum \alpha\beta(\alpha+\beta) = (\frac{5}{2})(2) - 3(\frac{3}{2})$ $= 5 - \frac{9}{2} = \frac{1}{2}$.

If $\alpha, \beta, \gamma$ are the roots of the equation $2x^3-5x^2+4x-3=0$,then $\sum \alpha \beta(\alpha+\beta)=$

Similar Questions

If $\sin 2 \theta$ and $\cos 2 \theta$ are solutions of $x^2+bx-c=0$,then

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,then what are the roots of the equation $cx^2 + bx + a = 0$?

If the roots of the equation $12x^2 - mx + 5 = 0$ are in the ratio $2 : 3$,then $m =$

If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be

If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module