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

Division of two like terms, Case 1: Suppose we have two terms 8ab and 4ab. ...

Case 1: Suppose we have two terms 8ab and 4ab. On dividing the first by the second we have 8ab/4ab = 2 or 4ab/8ab = (1/2) depending on whether we consider either 8ab or 4ab as the

Full asymptotic expansion , Consider the integral where the notatio...

Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri

How many cubic centimetres of cork dust will be required?, A cylindrical ve...

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between two vessels is fi

Time and Work, A and B can finish a piece of work in 16 days and 12 days re...

A and B can finish a piece of work in 16 days and 12 days respectively.A started a work and worked at it for 2 days.He was then joined by B.Find the total time taken to finish the

Determine the domain and range of function, Determine the domain of each of...

Determine the domain of each of the following functions.                         f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by

Find the probability , 1.  What is the probability that the two beverages w...

1.  What is the probability that the two beverages will be of the same kind? 2.  What is the probability that the two beverages will be different? 3.  What is the probability

Word problems, if I read 6 hours of spring break how many minutes did ...

if I read 6 hours of spring break how many minutes did read

Some important issue of graph, Some important issue of graph Before mov...

Some important issue of graph Before moving on to the next example, there are some important things to note. Firstly, in almost all problems a graph is pretty much needed.

Statistics Assignment, A. Design an investigation that details the followi...

A. Design an investigation that details the following six components:

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