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

Produt promotion, What is the structure of produt promotion?

What is the structure of produt promotion?

Calculate the profit, Lucas purchased his motorcycle for $5,875.98 and sold...

Lucas purchased his motorcycle for $5,875.98 and sold it for $7,777.77. What was his profit? To ?nd out the pro?t, you must subtract what Lucas paid for the motorcycle from the

Trigonometry, explain the formular for finding trigonometry

explain the formular for finding trigonometry

Decimals, how will the decimal point move when 245.398 is multiplied by 10

how will the decimal point move when 245.398 is multiplied by 10

Mod(z-25i)<15, Mod(Z-25i)   Sol) mod (Z-25i) means Z lies in the circumfer...

Mod(Z-25i)   Sol) mod (Z-25i) means Z lies in the circumference of the circle with (0,25) at its centre and radius less then 15. so difference in the max and min value of arg Z is

Evaluate subsequent proportion, Evaluate subsequent proportion: Examp...

Evaluate subsequent proportion: Example 2: If 5 pounds of apples cost 80 cents, how much will 7 pounds cost? Solution: By using x for the cost of 7 pounds of appl

Square root., i dont get these questions they are hard for me

i dont get these questions they are hard for me

Shares and dividends, at what price 6.25% rs 100 share be quoted when the m...

at what price 6.25% rs 100 share be quoted when the money is worth 5%

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