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

., There are k baskets and n balls. The balls are put into the baskets rand...

There are k baskets and n balls. The balls are put into the baskets randomly. If k

Initial value problem, An IVP or Initial Value Problem is a differential eq...

An IVP or Initial Value Problem is a differential equation with an appropriate number of initial conditions. Illustration 3 : The subsequent is an IVP. 4x 2 y'' + 12y' +

Find the area of the remaining part of cardboard, From a sheet of cardboard...

From a sheet of cardboard in the shape of a square of side 14 cm, a piece in the shape of letter B is cut off. The curved side of the letter consists of two equal semicircles & the

Reason why we start division, Reasons why we start division : The reason w...

Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we

Proof of constant times a function, Proof of Constant Times a Function: ...

Proof of Constant Times a Function: (cf(x))′ = cf ′(x) It is very easy property to prove using the definition given you a recall, we can factor a constant out of a limit. No

Example to understanidng of multiplication, 6-year-old Rahul wasn't able to...

6-year-old Rahul wasn't able to understand multiplication when it was thrust upon him in school. His mother discussed this problem with some of us. On the basis of suggestions that

What is the volume of this prism in terms of x, The area of the base of a p...

The area of the base of a prism can be expressed as x2 + 4x + 1 and the height of the prism can be expressed as x - 3. What is the volume of this prism in terms of x? Because t

Find the integral of a function, We want to find the integral of a function...

We want to find the integral of a function at an arbitrary location x from the origin. Thus, where I(x=0) is the value of the integral for all times less than 0. (Essenti

Type i and type ii errors-rejection and acceptance regions, Type I and type...

Type I and type II errors When testing hypothesis (H 0 ) and deciding to either reject or accept a null hypothesis, there are four possible happenings. a) Acceptance of a t

Evaluate performance of mental arithmetic maths, E 1) Try the two activitie...

E 1) Try the two activities detailed above with a few children around you Evaluate whether they really helped to improve the children's performance of mental arithmetic. Anot

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