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

Construction, draw a equilateral triangle with length of side 6.5 cm. and l...

draw a equilateral triangle with length of side 6.5 cm. and let us draw a parallelogram equal in area to that triangle and having an angle 45 degree

What is the purpose of the reparameterisation, We have independent observat...

We have independent observations Xi, for i = 1, . . . , n, from a mixture of m Poisson distributions with component probabilities d c and rates l c, for c = 1, . . . ,m. We decid

What is the probability of choosing a red ball, Q. What is the probability ...

Q. What is the probability of choosing a red ball? Ans. A box contains a red, blue and white ball. Two are drawn with replacement. (This means that one ball is selected, i

what is probability that point will be chosen from triagle, In the adjoini...

In the adjoining figure ABCD is a square with sides of length 6 units points P & Q are the mid points of the sides BC & CD respectively. If a point is selected at random from the i

Determine a meet b and a join b, Given A and B                 A =  |  1...

Given A and B                 A =  |  1  0  1  |         B =   |  1  1  0  |                       |  1  1  0  |                 |  0  1  1  |                       |  0

Equations of lines - three dimensional spaces, Equations of Lines In t...

Equations of Lines In this part we need to take a view at the equation of a line in R 3 .  As we saw in the earlier section the equation y = mx+b does not explain a line in R

Example of set theory, Suggest me the solution: Consider the given unive...

Suggest me the solution: Consider the given universal set T and its subjects C, D and E T = {0, 2, 4, 6, 8, 10, 12} C = {4, 8,} D = {10, 2, 0} E = {0} Find out

Power of iota, The next topic that we desire to discuss here is powers of i...

The next topic that we desire to discuss here is powers of i. Let's just take a look at what occurring while we start looking at many powers of i . i 1 = i

Range, identify the range of h(x)=2x+1

identify the range of h(x)=2x+1

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