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

A graph with a positive slope, A graph with a positive slope shows that the...

A graph with a positive slope shows that the variables depicted on the axes goes in the similar directions.

Probability, One coin is tossed thrice. what will be the probability of get...

One coin is tossed thrice. what will be the probability of getting neither 3 heads nor 3 tails

Determine the eigenvalues and eigenvectors of the matrix, Determine the eig...

Determine the eigenvalues and eigenvectors of the subsequent matrix. Solution : The first thing that we require to do is determine the eigen-values. It means we require

profit & loss, A sell a watch to B at gain of 20% and B sell to C at loss ...

A sell a watch to B at gain of 20% and B sell to C at loss of 10%. if C pays @ 432, how much did A pays for it.

Fermat''s theorem, Fermat's Theorem : If  f ( x ) contain a relative extre...

Fermat's Theorem : If  f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f

Homework, Euler''''s Constant (e) Approximate the number to the one hundred...

Euler''''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.

What is the connecticut sales tax on this item, Connecticut state sales tax...

Connecticut state sales tax is 6%. Lucy purchases a picture frame in which costs $10.50 What is the Connecticut sales tax on this item? Find out 6% of $10.50 by multiplying $10

If all the tickets are the similar price what was the cost, The total ticke...

The total ticket sales for a soccer game were $1,260; 210 tickets were purchased. If all the tickets are the similar price, what was the cost of a ticket? Divide the total sale

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