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

Probability, Question: There are 6 letters and 6 self addressed envelopes.W...

Question: There are 6 letters and 6 self addressed envelopes.What is the probability that atleast 1 is placed correctly?? Ans: If we let A be the event that letter A is in the cor

Define symmetric, Define symmetric, asymmetric and antisymmetric relations....

Define symmetric, asymmetric and antisymmetric relations.    Ans: Symmetric Relation A relation R illustrated on a set A is said to be a symmetric relation if for any x,

Find out the area of the circle, 1. The number of accidents attended to by ...

1. The number of accidents attended to by 6 emergency ambulance stations during a 5 month period was: Station May June July Aug Sep      A        21     20     22    37    37

Three dimensional geometry, Three Dimensional geometry Intorduction ...

Three Dimensional geometry Intorduction In earlier classes we studied about the coordinates in two planes that is the XY plane. Here we are going to study in detail about th

Applying quadratics math question, A boat tour company charges $11 for a ha...

A boat tour company charges $11 for a harbour tour and averages 450 passengers on Saturdays. Over the past few months, the company has been experimenting with the price of a tour a

Relative frequency definition, Relative Frequency  This type of probab...

Relative Frequency  This type of probability requires us to make some qualifications. We define probability of event A, occurring as the proportion of times A occurs, if we re

Which of the following binomials could represent the length, The area of Mr...

The area of Mr. Smith's rectangular classroom is x 2 - 25. Which of the following binomials could represent the length and the width of the room? Since area of a rectangle is

Integration, how to find area under a curve?

how to find area under a curve?

Linear equation, The ratio between the length and breadth of a rectangular ...

The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field

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