Select Page

## Competency in Focus: Root of Equation

This problem from Root of equation for B.Stat. (Hons.) Admission Test 2005 Objective Problem 2  is based on calculating a variable in a given equation.

## Next understand the problem

If $\sqrt{3}+1$ is a root of the equation $3x^{3}+ax^{2}+bx+12=0$ where a and b are rational numbers, then b is equal to (A) -6 (B) 2 (C) 6 (D) 10

### Algebra (Root of equation)

4/10
##### Suggested Book

Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics

Do you really need a hint? Try it first!
If the co effeicent of any polynomial equation is rational number and one of the root is a surd or coplex number, then the other root must be the conjugate.
Since our polynomial is of degree 3, there must be three roots of the equation. We already know the two of them so let the third one is $\gamma$.
we can use Vieta’s Theorem, that gives, the product of the roots is $\frac{c}{a}$ in our case $\frac{-12}{3}$ =$-4$. so we can say that $(1+\sqrt{3}) \times(1-\sqrt{3}) \times \gamma=-4$
Now we have calculated the value of gamma. Also we have from Vieta’s Theorem, that sum of products of the roots taken two roots at a time is $\frac{b}{3}$. So we can write,   $\frac{b}{3}=(1+\sqrt{3}) \times(1-\sqrt{3})+_{\gamma} \times\{(1+\sqrt{3})+(1-\sqrt{3})\}=2$.

## I.S.I. & C.M.I. Program

Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are: B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.
The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.

## The Mathematics of How Virus can Grow

The Mathematics of How Corona Virus Grow? The beautiful tale of undeterministic mathematics of chance and chaos of when they will become extinct or when they will thrive.

## The Exaggerated Triangle Inequality

Triangle Inequality is an exaggerated version of the Basic Idea of the Euclidean Plane. Let’s do some Triangle inequality Problems and Solutions.

## Geometric Median |Understand the concept

Geometric Median is an important concept in the intersection of Geometry, Data Analysis and Algorithms. This article explores the concept.

## Examples & Counterexamples – A Way to Build Your Own Mathematics

This is an interesting article on how to build your own Mathematics with the help of examples and counter examples. Stay tuned.

## Sets and Venn diagrams |B.Math Entrance

Try this beautiful problem from B.Math Entrance Exam based on sets and venn diagrams. You may use sequential hints to solve the problem.

## INMO 2007

Try to solve these interesting INMO 2007 Questions. Solve them and write the answers in the comment to check your answers.

## Order of General and Special Linear Group

Here is the post in which you would learn about the Order of General and Special Linear Group with the help of a problem. Try it and learn the solution.

## Maximizing Arrangements

Here is a post related to a problem based on maximizing arrangements in Mathematics. Try the problem and learn the solution.

## Gaps in Permutation | TOMATO Objective Problem

The simplest example of power mean inequality is the arithmetic mean – geometric mean inequality. Learn in this self-learning module for math olympiad

## Geometry of Tangents | ISI Entrance B.Stat 2009

Objective Problem Geometry (ISI Entrance) Find the radius of smaller circle. 01$\frac{3}{4}$2 Key Concepts 2D Geometry Similar Triangles Linear Equations Check the Answer Answer: $\frac{3}{4}$ ISI Entrance B.Stat Objective Problem, India Test of Mathematics at 10+2...