If a, b and c are the roots of x^3+4x+1=0,the | vedclass

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

Question

(C) Given that $a, b, c$ are the roots of the cubic equation $x^3+4x+1=0$. From Vieta's formulas,we have: $a+b+c = 0$ $ab+bc+ca = 4$ $abc = -1$ Since

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Given that $a, b, c$ are the roots of the cubic equation $x^3+4x+1=0$. From Vieta's formulas,we have: $a+b+c = 0$ $ab+bc+ca = 4$ $abc = -1$ Since $a+b+c = 0$,we can write: $a+b = -c$ $b+c = -a$ $c+a = -b$ Substituting these into the expression: $\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a} = \frac{1}{-c}+\frac{1}{-a}+\frac{1}{-b}$ $= -(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$ $= -(\frac{bc+ac+ab}{abc})$ $= -(\frac{4}{-1}) = 4$

If $a, b$ and $c$ are the roots of $x^3+4x+1=0$,then $\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}=$

Similar Questions

$A$ hyperbola passes through a focus of the ellipse $\frac{x^2}{169} + \frac{y^2}{25} = 1$. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of their eccentricities is $1$. Then,the equation of the hyperbola is:

Apical dominance is caused by

Which of the following compounds is an optically inactive compound?

$SO_{2}$ is a strong reducing agent; however,it can also act as an oxidising agent. Which of the following shows its oxidising nature?

Among the following,the least stable resonance structure is

Vedclass Test Series

Exam Paper Generator

Online Exam Module