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

What are the angles of depression from observing position, In Figure, what ...

In Figure, what are the angles of depression from the observing positions O 1 and O 2 of the object at A?

?, x/15=50/20

x/15=50/20

H, 6987+746-212*7665

6987+746-212*7665

Precalculus, describe the end behavior of the following function using Limi...

describe the end behavior of the following function using Limit notation f(x)= 2x-1/x-1

Discrete math, ) Show that the following argument is valid: (~p ? q) =>...

) Show that the following argument is valid: (~p ? q) => r s ? ~q ~t p => t (~p ? r) => ~s ------------------------ ? ~q 2) Show that the following argum

Two circles touching internally prove that ox:oy=oa:ob, Two circles touchin...

Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a

The fisher’s index, The Fisher's index The index of Fisher acts as a c...

The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.

Hyperboloid of two sheets - three dimensional spaces, Hyperboloid of Two Sh...

Hyperboloid of Two Sheets The equation which is given here is the equation of a hyperboloid of two sheets. - x 2 /a 2 - y 2 / b 2 + z 2 /c 2 = 1 Here is a diagram of

Integration and differentiation, Integration and Differentiation Diffe...

Integration and Differentiation Differentiation deals along with the determination of the rates of change of business activities or merely the process of finding the derivativ

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