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

Shortcuts, pls told the maths shortcuts

pls told the maths shortcuts

#titlealgebra.., help solve these type equations.-4.1x=-4x+4.5

help solve these type equations.-4.1x=-4x+4.5

Velocity of a skydiver (calculus), using v=g/k(1-e^-kt) find the velocity o...

using v=g/k(1-e^-kt) find the velocity of the skydiver when k is 0.015

Distance traveled by car - word problem, Distance Traveled by Car - word pr...

Distance Traveled by Car - word problem: It takes a man 4 hours to reach a destination 1325 miles from his home. He drives to the airport at an average speed of 50 miles per h

Harmonic mean-arthmetic geometric progression, Harmonic mean It is a m...

Harmonic mean It is a measure of central tendency which is utilized to determine the average increase rates for natural economies. This is defined like the reciprocal of the a

Find probability simulation, A reliability system consists of 15 independen...

A reliability system consists of 15 independent components. The probability that a component works is 0.9 for each. The system works if at least 11 of the components work. Fi

What is the measure of its width if its length is 3 inches, The perimeter o...

The perimeter of a rectangle is 21 inches. What is the measure of its width if its length is 3 inches greater than its width? Let x = the width of the rectangle. Let x + 3 = th

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 &

Find the determinant and inverse matrix, Find the Determinant and Inverse M...

Find the Determinant and Inverse Matrix (a) Find the determinant for A by calculating the elementary products. (b) Find the determinant for A by reducing the matrix to u

Solving an equation problems, Temperature: On one day in Fairfield, Montana...

Temperature: On one day in Fairfield, Montana the temperature dropped 80 degree fahrenheit from noon to midnight. If the temperature at midnight was -21 degree fahrenheit, write an

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