suppose that aii roots of the polynomial equation

x^4 - 4x^3 + ax^2 + bx + 1=0 are positive real numbers. show that all the roots of the polynomial are equal.

Question

suppose that aii roots of the polynomial equation x^4 - 4x^3 + ax^2 + bx + 1=0 are positive real numbers. show that all the roots of the polynomial are equal.

Swapnil Saxena · Answer

This can be solved by AM-GM inequality

Let the roots be a1,a2,a3,a4

Then a1*a2*a3*a4 = 1/1

Also (-1)(a1+a2+a3+a4) = -4/1= 4

If a1,a2,a3,a4 are all positive roots of the equation, applying AM-GM inequality

now if (a1+a2+a3+a4)/4= (a1*a2*a3*a4)^1/4 then essentially a1=a2=a3=a4

Then all rotts r equal

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

suppose that aii roots of the polynomial equation x^4 - 4x^3 + ax^2 + bx + 1=0 are positive real numbers. show that all the roots of the polynomial are equal.

suppose that aii roots of the polynomial equation

x^4 - 4x^3 + ax^2 + bx + 1=0 are positive real numbers. show that all the roots of the polynomial are equal.

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

suppose that aii roots of the polynomial equation x^4 - 4x^3 + ax^2 + bx + 1=0 are positive real numbers. show that all the roots of the polynomial are equal.

suppose that aii roots of the polynomial equation x^4 - 4x^3 + ax^2 + bx + 1=0 are positive real numbers. show that all the roots of the polynomial are equal.

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

suppose that aii roots of the polynomial equation

x^4 - 4x^3 + ax^2 + bx + 1=0 are positive real numbers. show that all the roots of the polynomial are equal.