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

Example of mathematical operations, Example of mathematical operations: ...

Example of mathematical operations: Example: Solve the following equation: [2 .( 3 + 5) - 5 + 2] x 3 =  ________   Solution: a.         Perform operations with

F distribution, The F Distribution The F distribution is the dis...

The F Distribution The F distribution is the distribution of the ratio of 2 random variables. Both random variables have yet another distribution, called the c 2 Distri

Solve following 4e1+3 x - 9e5-2 x = 0 logarithms, Solve following 4e 1+3 x...

Solve following 4e 1+3 x - 9e 5-2 x  = 0 . Solution Here the first step is to get one exponential on every side & then we'll divide both sides by one of them (that doesn'

Method of disks or the method of rings, Method of disks or the method of ri...

Method of disks or the method of rings One of the simple methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation.  Carrying out

What are factor trees explain, What are Factor Trees explain? In algebr...

What are Factor Trees explain? In algebra, we often need to factor a number into its prime factors. One way to do this is to use a factor tree. This is a network of numbers, st

Velocity of a skydiver (calculus), using v=g/k(1-e^-kt) find the velocity o...

using v=g/k(1-e^-kt) find the velocity of the skydiver when k is 0.015

Geometry, prove angle MJL is congruent to angle KNL

prove angle MJL is congruent to angle KNL

Give the introduction to ratios and proportions, Give the introduction to R...

Give the introduction to Ratios and Proportions? A ratio represents a comparison between two values. A ratio of two numbers can be expressed in three ways: A ratio of "one t

The service was wonderful how much is a 20% tip, Melisa and Jennifer threw ...

Melisa and Jennifer threw a fiftieth birthday party for their father at a local restaurant. While the bill came, Melisa added a 15% tip of $42. Jennifer said in which the service w

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