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

Calculus, What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at t...

What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at the point (4, f(4))

Basic operations for complex numbers, Now we have to discuss the basic oper...

Now we have to discuss the basic operations for complex numbers. We'll begin with addition & subtraction. The simplest way to think of adding and/or subtracting complex numbers is

Find the length of the second diagonal, Find the length of the second diago...

Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.

Trigonometry, if tan theta =1,find the value of sin4 theta + cos4 theta

if tan theta =1,find the value of sin4 theta + cos4 theta

Which of the subsequent numbers will yield a number larger, Which of the su...

Which of the subsequent numbers will yield a number larger than 23.4 while it is multiplied by 23.4? When multiplying through a number less than 1, you get a product in which i

Probability, I don''t understand the AND/OR rules and how they apply to pro...

I don''t understand the AND/OR rules and how they apply to probability

Evaluate limit, Evaluate the given limit. Solution: In this quest...

Evaluate the given limit. Solution: In this question none of the earlier examples can help us. There's no factoring or simplifying to accomplish.  We can't rationalize &

Statistics, explain the characteristics of statistics

explain the characteristics of statistics

Evaluate the slope of the line, Evaluate the slope of the line: Examp...

Evaluate the slope of the line: Example: What is the slope of the line passing through the points (20, 85) and (30, 125)? Solution:            m = 125 -85/30-20 = 4

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