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

6thgrade, do you have 3 digit and 4 digit number problem

do you have 3 digit and 4 digit number problem

Perimeter of trinagle, what is the perimeter of a triangele with the sides ...

what is the perimeter of a triangele with the sides of 32 in /22 in/20 in/

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

Mr F.D, how you divide 100 by 10 and then x by 10

how you divide 100 by 10 and then x by 10

Group automorphism, (a) Find an example of groups G, H, K with K  H and H...

(a) Find an example of groups G, H, K with K  H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve

Ratio and proportion, find the ratio of each of the following in simplest f...

find the ratio of each of the following in simplest form 1] 9 months to 7 by 4

Important points about the alternating series test, Important Points About ...

Important Points About the Alternating Series Test There are a several things to note about this test.  Very first, unlike the Integral Test and the Comparison or Limit Compari

AREA, How do you find the distributive property any faster?

How do you find the distributive property any faster?

Subsets of real numbers, is it true or false that all whole numbers are rat...

is it true or false that all whole numbers are rational numbers

Define period, Q. Define Period, Amplitude and Phase Shift? Ans. P...

Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest

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