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

Solve the inequality |x - 1| + |x - 2|, Solve the inequality |x - 1| + |x -...

Solve the inequality |x - 1| + |x - 2|≤ 3. Working Rule:    First of all measure the expression to zero whose modulus happens in the given inequation and from this search the va

Initial conditions to find system of equations, Solve the subsequent IVP. ...

Solve the subsequent IVP. y′′ + 11y′ + 24 y = 0 y (0) =0  y′ (0)=-7  Solution The characteristic equation is as r 2 +11r + 24 = 0 ( r + 8) ( r + 3) = 0

Scanning the demographic environment, I am working for supermarket chain an...

I am working for supermarket chain and responsible for the customer relationship management.The chain is planning to open exclusive thirst quenching service centers.These outlets w

Prove that r is an equivalence relation, 1. Let S be the set of all nonzero...

1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an

Derivatives, Derivatives The rate of change in the value of a...

Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is

Constructing tables versus rote learning maths, CONSTRUCTING TABLES VERSUS ...

CONSTRUCTING TABLES VERSUS ROTE LEARNING :  Ask any adult how she would help a child to acquire simple multiplication facts. There is a very strong possibility that she would say,

Weight, if an object weighed 11 pounds how many ounces would it weigh

if an object weighed 11 pounds how many ounces would it weigh

X and y -intercept, X-intercept  If an intercept crosses the x-axis we ...

X-intercept  If an intercept crosses the x-axis we will call it as x-intercept .  Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter

Algorithm for division helping a child grasp, E1) Why don't you think of so...

E1) Why don't you think of some activities for the same purpose now? E2) Suggest, in detail, another activity for helping a child grasp the algorithm for division. We come to

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