Prove that 2b3-3abc+a2d=0, Mathematics

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

Posted Date: 4/8/2013 2:14:38 AM | Location : United States

Related Discussions:- Prove that 2b3-3abc+a2d=0, Assignment Help, Ask Question on Prove that 2b3-3abc+a2d=0, Get Answer, Expert's Help, Prove that 2b3-3abc+a2d=0 Discussions

Write discussion on Prove that 2b3-3abc+a2d=0
Your posts are moderated
Related Questions
in triangle abc ab=ac and d is a point on side ac such that bc*bc=ac*cd. prove that bc=bd

Doing these sums initially in this way helps children see why they carry over numbers to the next column. You may like to devise some related activities now. , EI) Give activ

(a) Convert z  = - 2 - 2 i to polar form. (b) Find all the roots of the equation w 3 = - 2 - 2 i . Plot the solutions on an Argand diagram.

Evaluate the area of the shaded region in terms of π. a. 8 - 4π b. 16 - 4π c. 16 - 2π d. 2π- 16 b. The area of the shaded region is same to the area of the squa

If a single person makes $25,00 a year, how much federal income tax will he or she have to pay ?And they are gining me a chart that says $0 to $27,050 is 15% of taxes .

Data collected from the STATS 10x class survey one semester included responses to questions on the number of different sexual partners and on the number of pairs of shoes the stude

Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli

Can anybody provide me the solution of the following example? You are specified the universal set as T = {1, 2, 3, 4, 5, 6, 7, 8} And the given subjects of the universal s

if two circles O and O''intersect in two points, A and B, the the line segment OO is what?