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

Marketing management, successful marketing research relies on accurate iden...

successful marketing research relies on accurate identification of the research objectives. Critically discuss when setting relevant research objectives, drawing on marketing theor

Definition of infinite limits, Infinite limits : Let's now move onto the d...

Infinite limits : Let's now move onto the definition of infinite limits. Here are the two definitions which we have to cover both possibilities, limits which are positive infinity

Introducing counting, INTRODUCING COUNTING : From what you studied previou...

INTRODUCING COUNTING : From what you studied previous study, you know what it means to count. You would also agree that rote learning of number names does not always mean that the

Parenteral calculations, 850ml is to be administered to a person over 8 hou...

850ml is to be administered to a person over 8 hours using a drop factor of 20 drops/ml what is the flow rate in gtts/min ?

SHARES AND DIVIDEND, i am a student of class 10 and need help for making my...

i am a student of class 10 and need help for making my project on shares and dividend

Error in measurement, what is actual error and how do you calculate percen...

what is actual error and how do you calculate percentage error

Prove that the length of the altitude on the hypotenuse, If A be the area o...

If A be the area of a right triangle and b one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2  Ab /√ b 4 +4A 2 . An

Help, how do i know what operation to use in a fraction word problem

how do i know what operation to use in a fraction word problem

Theory of equations, If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(...

If p,q,r are roots of x^3-3x^2+4x-7=0 (p+2)(q+2)(r+2)=

Sequences and series - calculus, Sequences and Series In this section ...

Sequences and Series In this section we will be taking a look at sequences and infinite series.  In fact, this section will deal approximately exclusively with series.  Though

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