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

Factoring quadratic polynomials, Primary, note that quadratic is another te...

Primary, note that quadratic is another term for second degree polynomial. Thus we know that the largest exponent into a quadratic polynomial will be a2. In these problems we will

Lisa was assigned 64 pages how many more pages must she read, Lisa was assi...

Lisa was assigned 64 pages to read for English class. She has ?nished of the assignment. How many more pages must she read? If Lisa has read 3/4 of the assignment, she has 1/4

Differntial equation, (3x+2)^2 d^2y/dx^2+3(3x+2)dy/dx-36y=3x^2+4x+1

(3x+2)^2 d^2y/dx^2+3(3x+2)dy/dx-36y=3x^2+4x+1

Calculate values of kinetics , A reaction following first-order kinetics wa...

A reaction following first-order kinetics was studied by determining the reactant concentrations at equal time intervals. Each successive pair of concentrations, [A] o and [A] 1

Student, What is the slope and y intercept for (6,5) (-3,8)

What is the slope and y intercept for (6,5) (-3,8)

Solve 5x tan (8x ) =3x trig function, Solve 5x tan (8x ) =3x . Solution...

Solve 5x tan (8x ) =3x . Solution : Firstly, before we even begin solving we have to make one thing clear.  DO NOT CANCEL AN x FROM BOTH SIDES!!! Whereas this may appear like

The volume and surface area of this solid , The region bounded by y=e -x a...

The region bounded by y=e -x and the x-axis among x = 0 and x = 1 is revolved around the x-axis. Determine the volume and surface area of this solid of revolution.

Graph, Now we need to discuss graphing an equation. The first question whic...

Now we need to discuss graphing an equation. The first question which we have to ask is what accurately is a graph of an equation?  A graph is the set of all the ordered pairs whos

Probability and statistics, f Y is a discrete random variable with expected...

f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .

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