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

., There are k baskets and n balls. The balls are put into the baskets rand...

There are k baskets and n balls. The balls are put into the baskets randomly. If k

Fraction, sarah has 12 gel pen. she gave 3/4. how many she have

sarah has 12 gel pen. she gave 3/4. how many she have

How to dividing rational expressions, How to Dividing Rational Expressions ...

How to Dividing Rational Expressions ? To divide two fractions, or rational expressions, keep in Mind that division is the same as multiply by the Reciprocal of the second fra

What is the volume of the water required to fill the pool, A circular pool ...

A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =

Find the coordinates of the other two vertices, The two opposite vertices o...

The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

What is the maximum number calories which consume from fats, Josephine is o...

Josephine is on an 1,800 calorie per day diet. She tries to remain her intake of fat to no more than 30% of her overall calories. Based on an 1,800 calorie a day diet, what is the

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