If alpha+beta=-2 and alpha^3+beta^3=-56,then | vedclass

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

Question

(D) Given that,$\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$.We know that $\alpha^3+\beta^3 = (\alpha+\beta)(\alpha^2+\beta^2-\alpha\beta)$.Substitutin

Vedclass · Accepted Answer

$x^2+2x-8=0$

Vedclass · Answer

(D) Given that,$\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$.We know that $\alpha^3+\beta^3 = (\alpha+\beta)(\alpha^2+\beta^2-\alpha\beta)$.Substituting the values,we get $(-2)(\alpha^2+\beta^2-\alpha\beta) = -56$,which implies $\alpha^2+\beta^2-\alpha\beta = 28$.Also,$(\alpha+\beta)^2 = \alpha^2+\beta^2+2\alpha\beta = (-2)^2 = 4$.Subtracting the two equations: $(\alpha^2+\beta^2+2\alpha\beta) - (\alpha^2+\beta^2-\alpha\beta) = 4 - 28$.$3\alpha\beta = -24$,so $\alpha\beta = -8$.The quadratic equation with roots $\alpha$ and $\beta$ is given by $x^2 - (\alpha+\beta)x + (\alpha\beta) = 0$.Substituting the values,$x^2 - (-2)x + (-8) = 0$,which simplifies to $x^2+2x-8=0$.

If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$,then the quadratic equation whose roots are $\alpha$ and $\beta$ is

Similar Questions

Correct order of $3^{rd}$ Ionisation energy of $B, C, N$ and $O$ will be

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$ and $T$ is the tension in the string,then the net force on the particle (directed towards the centre) is

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

The major product of the following reaction is

Semi-water gas is a mixture of which of the following?

Vedclass Test Series

Exam Paper Generator

Online Exam Module