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

Npv, how to calculate the npv

how to calculate the npv

Statistics, find the number of ways 17 employees can b chosen from 327

find the number of ways 17 employees can b chosen from 327

Scientific notation, kikos toy company boasts that their remotes have the g...

kikos toy company boasts that their remotes have the greatest range . their claim is that you can access their signal up to 1320 feet from their device . a competing company, yozzo

#title., am i going to get As

am i going to get As

Cluster sampling, Cluster Sampling Cluster sampling is where a few geog...

Cluster Sampling Cluster sampling is where a few geographical regions for illustration, a location, village or town are selected at random and say every single household or sho

Evaluate the volume of a ball, Evaluate the volume of a ball whose radius i...

Evaluate the volume of a ball whose radius is 4 inches? Round to the nearest inch. (π = 3.14) a. 201 in 3 b. 268 in 3 c. 804 in 3 d. 33 in 3 b. The volume of a

Algebra, solutions for the equation a-b=5

solutions for the equation a-b=5

Bounded intervals, Let a and b be fixed real numbers such that a ...

Let a and b be fixed real numbers such that a The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all r

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