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

Evaluate the linear equation, Evaluate the linear equation: Solve the ...

Evaluate the linear equation: Solve the equation ax - b = c for x in terms of a, b, and c. Solution: Step 1. Using Axiom 1, add b to both sides of the equation. a

Explain lobachevskian geometry and riemannian geometry, Explain Lobachevski...

Explain Lobachevskian Geometry and Riemannian Geometry ? Nineteenth century mathematician Nicolai Lobachevsky assumed that the summit angles of a Saccheri quadrilateral are ac

Saddle point-game theory, Saddle Point This point in a pay off matrix i...

Saddle Point This point in a pay off matrix is one which is the largest value in its column and the smallest value in its row. This is also termed as equilibrium point in the t

Process for solving linear equations, 1. If the equation has any fractions ...

1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al

Polynomials in one variable, Polynomials In this section we will discu...

Polynomials In this section we will discuss about polynomials.  We will begin with polynomials in one variable. Polynomials in one variable Polynomials in one variable

POLYNOMIAL, HOW WE CAN FACTORISE 12X+7X+1

HOW WE CAN FACTORISE 12X+7X+1

Show that 571 is a prime number, Show that 571 is a prime number. Ans: ...

Show that 571 is a prime number. Ans:    Let x=571⇒√x=√571 Now 571 lies between the perfect squares of  (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1

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