If the roots ff the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 are equal, then prove that either a = 0 or a3 + b3 + c3 = 3abc"

Asked by Last Modified  

5 Answers

Learn Mathematics +1 Class IX-X Tuition

Follow 6
Answer

Please enter your answer

Mainak Das

Tutor

u can do this problem with the help of SHIDHARACHARYA formula which is ax2=bx+c=0
Comments
Dislike Bookmark

apply shri dharacharai identity....when both roots are equal B^2-4AC=0 ..........(1) HERE B=-2(a^2-bc), A=c^2-ab, C=b^2-ac now apllying the conditions,and put all these values in eqn (1) we get 4(a^2-bc)^2-4(c^2-ab)(b^2-ac)=0 a^4+b^3+c^3-3a^2bc=0 by taking common a from above eqn we get what...
read more
apply shri dharacharai identity....when both roots are equal B^2-4AC=0 ..........(1) HERE B=-2(a^2-bc), A=c^2-ab, C=b^2-ac now apllying the conditions,and put all these values in eqn (1) we get 4(a^2-bc)^2-4(c^2-ab)(b^2-ac)=0 a^4+b^3+c^3-3a^2bc=0 by taking common a from above eqn we get what we have to prove it a=0 or a^3+b^3+c^3=3abc read less
Comments
Dislike Bookmark

Eco, Maths and Stats Tutor

Basically, remember for a quadratic equation Ax^2 + Bx +C=0, the two roots are equal only if B^2 - 4AC=0. In the given equation, A=(c^2 - ab), B = -2(a^2-bc) and C = b^2 - ac. Substitute these values in the relation B^2 =4AC and simplify to get the desired result.
Comments
Dislike Bookmark

(a^2-bc)^2=(c^2-ab)(b^2-ac) a(a^3-2abc)=a(-b^3-c^3+abc) a=0(or)a^3+b^3+c^3=3abc
Comments
Dislike Bookmark

Good basic mathematics, Basic electronics, VLSI, Basic technical knowledge

Both roots are equal=> D=0 => b2-4ac=0=> 4 (a2-bc)2-4 (c2-ab)(b2-ac)=0 =>a4-2a2bc+b2c2-b2c2+c3a+b3a-a2bc=0 => a (a3+b3+c3-2abc-abc)=0; for the equation to be 0, either a=0 or a3+b3+c3-3abc=0 ; so a=0 or a3+b3+c3=3abc
Comments
Dislike Bookmark

View 3 more Answers

Related Questions

How many edges are there in a cylinder?
2 edges.
Thileshwari
0 0
View Comments6
Find the number of terms of the A.P: 7, 13, 19, ...., 205?
The first term, t1=a = 7. The common difference, b=13 - 7=6. Last term or the nth term, tn=a + (n-1)b = 205. So, we have, 7 + (n - 1)6 = 205 --> (n - 1) = (205 - 7)/6 = 33 --> n = 34. Answer: Number of terms is 34.
Swati
0 0
View Comments6
What is indeterminate form? Please explain.
Indeterminate means the number or expression we cant determine. i.e. 0/0 , infinity/infinity. Etc.
Akanksha
Which is best book for preparing algebra for JEE?
1)Objective Mathematics by R.D. Sharma 2)Algebra by Dr. S.K. Goyal 3)Arihant's Algebra for JEE Main and Advanced by Dr. SK Goyal.
User
0 0
View Comments8
What is algebraic geometry?
Algebraic geometry is a branch of mathematics that studies the solution sets of polynomial equations. It uses tools from both algebra and geometry to study geometric objects, such as curves and surfaces, that can be defined by polynomial equations.
Franziska
0 0
View Comments7

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

Ask a Question

Related Lessons

Class-10 L-4 Quadratic Equations Ex-4.1 Q1 (vii)

Ashish Bhatia

0 0
View Comments0
Similarity vs Congruency
Similar figures and congruent figures both have the same shape. Two triangles are congruent if they are the same size and shape. Congruency:They are exactly same in length, width, shape, size etc. They...

Raj Kumar

0 0
View Comments0
Class-10 L-4 Quadratic Equations Ex-4.1 Q1 (i) (ii)

Ashish Bhatia

0 0
View Comments0
Real Numbers notes summary
Class 10 Mathematics – Real Numbers Notes (Conceptual) 1. Introduction Real numbers are all the numbers that can be represented on the number line. They include: Rational numbers...

Sujoy Das

0 0
View Comments0
class-10 L-6 Triangles Ex-6.2 Q5

Ashish Bhatia

0 0
View Comments0

Recommended Articles

Meet Sandhya R, a B.Sc tutor from Bangalore

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 >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Meet Raghunandan.G.H, a B. Tech Tutor from...

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 >

Quest Academy - Institute of the month

Quest Academy is a professional Bangalore based NEET and JEE (Main + Advanced) training institute. The academy was incorporated in 2015 to cater to the needs of students, who aim to crack competitive exams by connecting with the best brains around. The institute helps students enhance their skills and capabilities through...

Read full article >

Find Class 10 Tuition near you
Class 10 Tuition in Delhi
Class 10 Tuition in Bangalore
Class 10 Tuition in Hyderabad
Class 10 Tuition in Kolkata
Class 10 Tuition in Mumbai
Class 10 Tuition in Chennai
Class 10 Tuition in Pune
Class 10 Tuition in Lucknow
Class 10 Tuition in Noida
Class 10 Tuition in Jaipur
Online Tuition Class 10

Looking for Class 10 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you