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

Define universal set, Q. What is set theory? Define universal set? Ans...

Q. What is set theory? Define universal set? Ans. The  universe , or  universal set , written as  U , is the set that contains all elements being considered in a given dis

Calculate the probability - contingency table, 1) A survey was done where a...

1) A survey was done where a random sample of people 18 and over were asked if they preferred comedies, dramas, or neither. The information gathered was broken down by age group an

Definition of infinite limits, Infinite limits : Let's now move onto the d...

Infinite limits : Let's now move onto the definition of infinite limits. Here are the two definitions which we have to cover both possibilities, limits which are positive infinity

Amy purchased 6 books how much did the books cost altogether, Amy purchased...

Amy purchased 6 books at $4.79 each. How much did the books cost altogether? Multiply 6 by $4.79; 6 × $4.79 = $28.74.

Calculate the area of the skirt to the nearest foot, Pat is making a Christ...

Pat is making a Christmas tree skirt. She needs to know how much fabric to buy. Using the example provided, calculate the area of the skirt to the nearest foot. a. 37.7 ft 2

Which team should get the ball at the beginning, Why is tossing a coin cons...

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a foot ball match? Ans: equally likely because they are mutual

Total linear attenuation, Consider the task of identifying a 1 cm thick bre...

Consider the task of identifying a 1 cm thick breast cancer that is embedded inside a 4.2 cm thick fibroglandular breast as depicted in Fig. The cancerous tumor has a cross

Logorithms, log base 5 (3-2x) + log base 5 (2+x) = 1

log base 5 (3-2x) + log base 5 (2+x) = 1

Rounding, what is the nearest ten thousand of 92,892?

what is the nearest ten thousand of 92,892?

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