Find the polynomial zeros , Mathematics

Assignment Help:

If two zeros of the polynomial f(x) = x4 - 6x3 - 26x2 + 138x - 35 are 2 ± √3.Find the other zeros.     (Ans:7, -5)

Ans: Let the two zeros are 2 +√3 and 2 - √3

Sum of Zeros       = 2 + √3 + 2 - √3

= 4

Product of Zeros = ( 2+√3 )(2 - √3 )

= 4 - 3

= 1

Quadratic polynomial is x2 - (sum) x + Product

2088_divisiom.png

 

                  x4 - 4 x3 + x2

                 -----------------

                 -2x3 - 27x2 + 138x

                 - 2x3 + 8x2 - 2x

                -----------------------

                -35x2 + 140x - 35

                -35x2 + 140x - 35

                ------------------------

                    0

                ------------------------

∴ x2 - 2x - 35 = 0

(x - 7)(x + 5) = 0

x = 7, -5

other two Zeros are 7 and -5


Related Discussions:- Find the polynomial zeros

Find out indegree, Question: Consider a digraph D on 5 nodes, named x0...

Question: Consider a digraph D on 5 nodes, named x0, x1,.., x4, such that its adjacency matrix contains 1's in all the elements above the diagonal A[0,0], A[1,1], A[2,2],.., e

Duality, how management making future decition by using duality

how management making future decition by using duality

Example of hcf, Example  Find the Highest Common Factor of 54, 72...

Example  Find the Highest Common Factor of 54, 72 and 150. First we consider 54 and 72. The HCF for these two quantities is calculated as follows:

Difererntial equation, Ask queFind the normalized differential equation whi...

Ask queFind the normalized differential equation which has {x, xex} as its fundamental setstion #Minimum 100 words accepted#

Geometry, RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS...

RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS, ST, AND RT

Progressions, what value of k is he sequence 2k+4,3k-7,k+12 are in an arith...

what value of k is he sequence 2k+4,3k-7,k+12 are in an arithmetic sequence is

Numertic methods, solve by factorization method; 10x-6y-3z=100, -6x+10y-5z=...

solve by factorization method; 10x-6y-3z=100, -6x+10y-5z=100, -3x-5y+10z=100

''t'' distribution, The 't' distribution is a theoretical probability distr...

The 't' distribution is a theoretical probability distribution. The 't' distribution is symmetrical, bell-shaped, and to some extent similar to the standard normal curve. It has an

Algorithm for division, Also, their inability to apply the algorithm for di...

Also, their inability to apply the algorithm for division becomes quite evident. The reason for these difficulties may be many. We have listed some of them below. 1) There are n

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