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

Find fourier series, Question: Find Fourier series for the periodic fun...

Question: Find Fourier series for the periodic function of period 2 π,defined by      f(x) = x 4 ,  - π ≤ x ≤ π

Stakeholders, what is the benefit for stakeholders or disadvantage in a mon...

what is the benefit for stakeholders or disadvantage in a monoply

Reduce the rational expression to lowest terms, Reduce the following ration...

Reduce the following rational expression to lowest terms.                                     x 2 - 2 x - 8/ x 2 - 9 x + 20 Solution When reducing a rational expressio

Arthemetic progreession, ball are arranged in rows to form an equilateral t...

ball are arranged in rows to form an equilateral triangle .the firs row consists of one abll,the second of two balls,and so on.If 669 more balls are added,then all the balls canbe

Example of inverse matrix, Determine the inverse of the following matrix, i...

Determine the inverse of the following matrix, if it exists. We first form the new matrix through tacking onto the 3 x 3 identity matrix to this matrix.  It is, We

Differentiate outline function in chain rules, Differentiate following. ...

Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2

Differentiate y = x x using implicit differentiation, Differentiate y = x ...

Differentiate y = x x Solution : We've illustrated two functions similar to this at this point. d ( x n ) /dx = nx n -1                                 d (a x ) /dx= a

Maths Assessment, Assessment task This Term Assessment will require you ass...

Assessment task This Term Assessment will require you assess the effectiveness of your current lunch budget and prepare a proposal to your caregiver to seek permission to be given

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