If the roots of the equation 4x^3 - 12x^2 + 1 | vedclass

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

Question

(A) Let the roots of the equation $4x^3 - 12x^2 + 11x + k = 0$ be $\alpha - d, \alpha, \alpha + d$. By Vieta's formulas,the sum of the roots is given

Vedclass · Accepted Answer

$-3$

Vedclass · Answer

(A) Let the roots of the equation $4x^3 - 12x^2 + 11x + k = 0$ be $\alpha - d, \alpha, \alpha + d$. By Vieta's formulas,the sum of the roots is given by: $(\alpha - d) + \alpha + (\alpha + d) = -\frac{-12}{4} = 3$. $3\alpha = 3 \Rightarrow \alpha = 1$. Since $\alpha = 1$ is a root of the equation,it must satisfy $4(1)^3 - 12(1)^2 + 11(1) + k = 0$. $4 - 12 + 11 + k = 0$. $3 + k = 0 \Rightarrow k = -3$.

If the roots of the equation $4x^3 - 12x^2 + 11x + k = 0$ are in arithmetic progression,then $k$ is equal to

Similar Questions

The transformed equation of $3x^2 + 3y^2 + 2xy = 2$,when the coordinate axes are rotated through an angle of $45^{\circ}$,is

Eubacteria is an example of which domain?

An $\alpha$-particle of energy $E$ is liberated during the decay of a nucleus of mass number $236$. The total energy released in this process is

Which of the following cannot be used in Friedel-Crafts reactions?

The area bounded by the parabola $y=x^2$ and the line $y=x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module