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

Comparing and scaling, a dairy mngr says it takes 70lbs of make 10 lbs of c...

a dairy mngr says it takes 70lbs of make 10 lbs of cottage cheese... How do I make a rate table and a make a graph showing the relationship between lbs of milk and lbs of cottage c

If the area of the parallelogram is 36 m2 what is the height, The height of...

The height of a parallelogram measures 5 meters more than its base. If the area of the parallelogram is 36 m 2 , what is the height in meters? Let x = the measure of the base a

Operation research, difference between scope and application of operation r...

difference between scope and application of operation research

Derivatives with chain rule, Chain Rule : We've seen many derivatives...

Chain Rule : We've seen many derivatives.  However, they have all been functions similar to the following kinds of functions. R ( z ) = √z      f (t ) = t 50

Solve the subsequent differential equation, Solve the subsequent differenti...

Solve the subsequent differential equation. 2xy - 9 x 2 + (2y + x 2 + 1) dy/dt = 0 Solution Let's start off via supposing that wherever out there in the world is a fun

Pi, pi to the ten-thousandths

pi to the ten-thousandths

Find the tangent to the curve, 1. Find the third and fourth derivatives of ...

1. Find the third and fourth derivatives of the function Y=5x 7 +3x-6-17x -3 2. Find the Tangent to the curve Y= 5x 3 +2x-1 At the point where x = 2.

Derivatives, What are the ingredients of a Mathematical Model? What is a mo...

What are the ingredients of a Mathematical Model? What is a model?

Ratios, What is the ratio of the cone''s volume to the cylinder''s volume

What is the ratio of the cone''s volume to the cylinder''s volume

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