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 locus of the centre of a circle which passes through the origin and cuts off a chord of length $4$ units from the line $x=3$ is

Which of the following noble gases has the highest polarizability?

Which of the following enzymes hydrolyzes the internal phosphodiester bonds in a polynucleotide chain?

What is the megasporangium also known as?

In which of the following production processes is limestone $(CaCO_3)$ $NOT$ used?

Vedclass Test Series

Exam Paper Generator

Online Exam Module