prove that 2a=b+c, Mathematics

Assignment Help:

If the roots of the equation (a-b)x2 + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c.

Ans:    (a-b)x2 + (b-c) x+ (c - a) = 0

T.P 2a = b + c

B2 - 4AC = 0

(b-c)2 - [4(a-b) (c - a)] = 0

b2-2bc + c2 - [4(ac-a2 - bc + ab)] = 0

⇒ b2-2bc + c2 - 4ac + 4a2 + 4bc - 4ab = 0

⇒ b2+ 2bc + c2 + 4a2 - 4ac - 4ab= 0

⇒ (b + c - 2a)2 = 0

⇒ b + c  = 2a

 


Related Discussions:- prove that 2a=b+c

Calculate the radius of the circle, In the figure, ABCD is a square inside ...

In the figure, ABCD is a square inside a circle with centre O. The Centre of the square coincides with O & the diagonal AC is horizontal of AP, DQ are vertical & AP = 45 cm, DQ = 2

Arithmetic/Geometric Sequences and Binomial Expansion, Find the 35th term o...

Find the 35th term of the sequence in which a1 = -10 and the common difference is 4.

Prove that sinx+cosx=? , Multiply and divide by root2, then root2/root2...

Multiply and divide by root2, then root2/root2(sinx+cosx) = root2(sinx/root2 + cosx/root2) = root2(sinx cos45+cosx sin45) = root2(sin(x+45))

Wave through the origin always has a slope of one or not, Can you explain t...

Can you explain that a wave through the origin always has a slope of one or not?

Linear Programming, A garden shop wishes to prepare a supply of special fer...

A garden shop wishes to prepare a supply of special fertilizer at a minimal cost by mixing two fertilizers, A and B. The mixture is to contain at least 45 units of phosphate at lea

Constant aceleration formulae, a car comes to a stop from a speed of 30m/s ...

a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p

Objectives of multiplication and division, Objectives After reading t...

Objectives After reading this unit, you should be able to 1. Explain the meaning of multiplication / division and interpret it in different contexts; 2. Convert symbo

Find ways in which prizes are distributed between student, Find out the num...

Find out the number of ways in which 5 prizes can be distributed among 5 students such that  (a)   Each student may get a prize. (b)  There is no restriction to the number o

Math, the size of my sitting room is 7metres by 6metres . i bought a rug fo...

the size of my sitting room is 7metres by 6metres . i bought a rug for covering the centre of its floor. one metre of the floor around the edge of the room is not to be covered by

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd