UrbanPro

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

If AM and GM of roots of a quadratic equation are 6 and 4 respectively, then find out the quadratic equation and solve it.

Asked by Last Modified  

Follow 1
Answer

Please enter your answer

Tutor

Let the root of quadratic eqn are a and b As given in question AM=(a+b)/2=6 =>a+b=12-----------------(eqn 1) GM=square root of (ab)=4 =>ab=16--------------(enq 2) As you know quadratic eqn is given by:- X^2-(sum of roots)X+product of roots=0 i.e X^2-(a+b)X+ab=0 from eqn 1 and egn 2 X^2-12x+16=0 this...
read more
Let the root of quadratic eqn are a and b As given in question AM=(a+b)/2=6 =>a+b=12-----------------(eqn 1) GM=square root of (ab)=4 =>ab=16--------------(enq 2) As you know quadratic eqn is given by:- X^2-(sum of roots)X+product of roots=0 i.e X^2-(a+b)X+ab=0 from eqn 1 and egn 2 X^2-12x+16=0 this is the required eqn... read less
Comments

Tutor

If A and B are roots of a quadratic equation, then the equation can be written as follow:- x^2 - (A+B)x + (A*B)=0. It is given that the arithmetic mean of the roots is 6. This means... (A+B)/2 =6 further implying (A+B) =12. Also the geometric mean of the roots is given as 4. this means... square...
read more
If A and B are roots of a quadratic equation, then the equation can be written as follow:- x^2 - (A+B)x + (A*B)=0. It is given that the arithmetic mean of the roots is 6. This means... (A+B)/2 =6 further implying (A+B) =12. Also the geometric mean of the roots is given as 4. this means... square root of (A*B)=4, Therefore A*B =16. Hence, the quadratic equation is x^2-12x+16=0. Roots of a quadratic equation of the form a(x^2)+bx+c=0 is given by x= [-b+ sqrt(b^2)-4ac)]/2a and [-b- sqrt(b^2)-4ac)]/2a. Here a=1, b= -12 and c=16. putting this we get, x= [12 + sqrt(144-64)]/2 and [12 - sqrt(144-64)]/2, = [12 + sqrt(80)]/2 and [12 - sqrt(80)]/2 = [12 + sqrt(16*5)]/2 and [12 + sqrt(16*5)]/2 taking 16 outside the sqrt sign = [12 + 4sqrt(5)]/2 and [12 - 4sqrt(5)]/2 now simplify by dividing each term of numerator (separated by + sign) by denominator x=6+2sqrt(5) and 6-2sqrt(5). NOTE:- sqrt here refers to operation of taking square root. read less
Comments

Tutor

x2-12x+16
Comments

Learn Mathematics from an IITian

The quadratic equation is x² - 12x +16 = 0, and the roots are (6 - 2?5) and (6 + 2?5)
Comments

Online Tutor-Mathematics, Science, Competitive Exam Preparation

6+2?5, 6-2?5 are the roots Quadratic equation is x2-12x-16=0 Hint Sum of roots = -b/a = AM*2 Product of roots = c/a = GM^2
Comments

Matrix MATH

Let, roots are a and b. So Equation is : (x-a)(x-b)=0 => x^2 --a.x-b.x +a.b=0=> x^2 --(a+b)x + a.b=0---- (1) According to the question, AM=(a+b)/2= 6=> a+b=12 GM=?(a.b)=4 => a.b= 16. Substituting these in (1), The required quadratic equation is: x^2 --12x+16=0, To solve the equation, use Shridharacharya’s...
read more
Let, roots are a and b. So Equation is : (x-a)(x-b)=0 => x^2 –a.x-b.x +a.b=0=> x^2 –(a+b)x + a.b=0---- (1) According to the question, AM=(a+b)/2= 6=> a+b=12 GM=?(a.b)=4 => a.b= 16. Substituting these in (1), The required quadratic equation is: x^2 –12x+16=0, To solve the equation, use Shridharacharya’s Formula read less
Comments

"Empowering Minds with 12+ Years of Expertise in Computer Science & Mathematics - Learn with Rajesh"

Put The AM as b and GM as c in standard form.
Comments

Mathematics for JEE Mains/Advanced, XI & XII (All Boards)

Clearly as you have suggested if a and b are the roots then: (a+b)/2 = 6 and (ab)^0.5 = 4. Now by theory of equations it is clear that solution is x² - (a+b)x + ab = 0
Comments

Mathematics Teacher

x^2 -12x +16 =0
Comments

Make mathematics Interesting

let quadratic equation is ax^2 + bx+c = 0 ---(1) and it's roots are X1 and X2. As per given condition X1 + X2 = 2 * 6 = 12. X1 * X2 = (4) ^2 = 16. As X1 and X2 are the roots of above quadratic equation, it's relation with coefficient's of equation (a,b,c) is X1+X2 = (-b/a) and X1 * X2 = (c/a). Here...
read more
let quadratic equation is ax^2 + bx+c = 0 ---(1) and it's roots are X1 and X2. As per given condition X1 + X2 = 2 * 6 = 12. X1 * X2 = (4) ^2 = 16. As X1 and X2 are the roots of above quadratic equation, it's relation with coefficient's of equation (a,b,c) is X1+X2 = (-b/a) and X1 * X2 = (c/a). Here we are having values of (b/a) and (c/a) thus simply divide equation (1) by a (a is non zero). x^2 + (b/a) x + (c/a) = 0. x^2 -12x + 16 = 0. By solving this roots will be (6 + 2 sqrt(5)) and (6 - 2 sqrt (5)). Hope it is clear :-). read less
Comments

View 12 more Answers

Related Questions

In how many ways can the letters of the word "ASSASSINATION" be arranged so that all the S's are together ?
Group all 's' together and call it X remaining letters have 3A, 2I, 2N, one T and one O so total letters = 10 out of this 3! terms will have indistinguishable 'A' 2! indistinguishable 'I' and same...
Kumar Upendra Akshay
What is O level Coaching?
Although your question is not specific,but there is a course called o level conducted by DOECC, now well known as national institutE of electronics and it.four paper are there c language, architecture,...
Ajay
What is direction of friction on front and back wheel of cycle?
In bicycle, pedalling is done on rear wheel. This means that we try to rotate the rear wheel to move forward. The rear wheel pushes the ground backwards and gets the forward frictional force which pushes...
Ravi Ranjan

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Introduction To Accounting: Part 19: Verifiable Objective Concept
The Verifiable Objective Concept holds that accounting should be free from personal bias. Measurements that are based on verifiable evidences are regarded as objectives. It means all accounting...

KEY TO SUCCESS
Positive thinking make your energy and your environment positive.Sometimes we are facing many problems simultaneously and some problems which are unexpected, we should be calm and try to solve them by...
M

Mohit S.

2 0
0


Sets
A set is a well defined collection of objectives. A = {coat, hat, scarf, gloves, boots}, where A is the name of the set, and the braces indicate that the objects written between them belong to the set. Every...

SPECIAL EVENTS IN PARTNERSHIP
SPECIAL EVENTS IN PARTNERSHIP Admission Retirement Death Change in Ratio Combination When a New partner is admitted what are the changes occur? What are the things unavoidable changes? Can...

Recommended Articles

Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...

Read full article >

Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition.  Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...

Read full article >

Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...

Read full article >

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more