Prove that 2b3-3abc+a2d=0, Mathematics

Assignment Help:

If  the  ratios  of  the  polynomial ax3+3bx2+3cx+d  are  in  AP,  Prove  that  2b3-3abc+a2d=0

Ans: Let p(x) = ax3 + 3bx2 + 3cx + d and α , β , r are their three Zeros but zero are in AP

let α = m - n , β = m, r = m + n

sum = α+β+ r = - b/a

substitute this sum , to get = m= -b/a

Now taking two zeros as sum αβ +β r +αr =  c a

(m-n)m + m(m+n) + (m + n)(m - n) = 3c/a

Solve this problem , then we get

3b2  - 3ac/a2 = n2

 

Product αβ r = d/ a

(m-n)m (m+n) = -d/a

(m2 -n2)m = - d/a

[(-b/a)2-(3b2 -3ac/a2)](-b/a) = -d/a

Simplifying we get

2b3 - 3abc + a2 d = 0


Related Discussions:- Prove that 2b3-3abc+a2d=0

Integration, R={(r, ?):1=r= 2cos? ,-p/3= ? =p/3

R={(r, ?):1=r= 2cos? ,-p/3= ? =p/3

Describe segments, Describe Segments, Rays, Angles, and Triangles We now...

Describe Segments, Rays, Angles, and Triangles We now define some more basic geometric figures. 1. Segments Definition A segment is the set of two given points and all the

Graphs, How do I graph a round robin pool tournment with 6 players using gr...

How do I graph a round robin pool tournment with 6 players using graph theory

Matrix, parts of matrix and functions

parts of matrix and functions

Proportions, bananas are on sale for 3 pounds for $2. At that price how man...

bananas are on sale for 3 pounds for $2. At that price how many pounds can you buy for $22

Krystal, what is the tenths place

what is the tenths place

Determine the probability - conditional probability, A bag of 28 tulip bulb...

A bag of 28 tulip bulbs contains 12 red tulip bulbs, 9 yellow tulip bulbs, and 7 purple tulip bulbs. Two bulbs are selected without replacement. Determine, a) The probability th

Example of integration by parts - integration techniques, Example of Integr...

Example of Integration by Parts - Integration techniques Illustration1:  Evaluate the following integral. ∫ xe 6x dx Solution : Thus, on some level, the difficulty

Multiple linear regression models, Multiple Linear Regression Models T...

Multiple Linear Regression Models There are situations whether there is more than one factor which influence the dependent variable Illustration Cost of production weekl

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

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