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
weather prediction on monsoon past data on project


Statistical inference This is the process of drawing conclusions about attributes of a population based upon information contained in a sample or taken from the population.

Randi takes the stairs at work whenever possible instead of the elevator. She must climb up 51 steps from her office to get to the accounting department. The human resources depa


solve the parameter estimate in v=a+bx+cx^2

Business Applications In this section let's take a look at some applications of derivatives in the business world.  For the most of the part these are actually applications wh


2(x+3x)+(x+3x)

1.If a+b=2b and ab+cd+ad=3bc,prove that a,b,c,d are in A.P 2.The nth term of an A.P is an+b.Find the sum of the series upto n terms.