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

Differential equation, Suppose a fluid (say, water) occupies a domain D? R^...

Suppose a fluid (say, water) occupies a domain D? R^(3 ) and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid

Geometry, the segments shown could form a triangle

the segments shown could form a triangle

Iit-jee questions, can u tell me a website for iit-jee questions?

can u tell me a website for iit-jee questions?

Hydrostatic pressure and force - applications of integrals, Hydrostatic Pre...

Hydrostatic Pressure and Force - Applications of integrals In this part we are going to submerge a vertical plate in water and we wish to know the force that is exerted on t

Shares and dividends, how to see shares and dividends of a company and are ...

how to see shares and dividends of a company and are they seen day wise?

Pre-operational stage-development learning maths, Pre-operational Stage : ...

Pre-operational Stage :  This period of a child's cognitive development usually begins at the age of 2, and lasts until about the age of 6. Thus, it usually coincides with the pre

How to multiplying monomials, How to Multiplying Monomials? To multiply...

How to Multiplying Monomials? To multiply monomials: Step 1: Multiply the coefficients. Step 2: Multiply the like variables by adding their exponents. Step 3: Multiply ans

Ratio and proportion, find the ratio of each of the following in simplest f...

find the ratio of each of the following in simplest form 1] 9 months to 7 by 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