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

Integration variable, Integration variable : The next topic which we have ...

Integration variable : The next topic which we have to discuss here is the integration variable utilized in the integral. In fact there isn't actually a lot to discuss here other

Differential Equations, 1.Verify Liouville''s formula for y "-y" - y'' + y ...

1.Verify Liouville''s formula for y "-y" - y'' + y = 0 in (0, 1) ? 2.Find the normalized differential equation which has {x, xex} as its fundamental set. 3.6Find the general soluti

Limits, Limits The concept of a limit is fundamental in calculus....

Limits The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some

Product moment coefficient (r), Product Moment Coefficient (r) ...

Product Moment Coefficient (r) This gives an indication of the strength of the linear relationship among two variables.                                     N

Calculate the ratio of the areas of three sectors, A circular disc of 6 cm ...

A circular disc of 6 cm radius is divided into three sectors with central angles 1200, 1500,900. What part of the circle is the sector with central angles 1200. Also give the ratio

Formula to estimate distance around circle table, If Lisa wants to know the...

If Lisa wants to know the distance around her circular table, that has a diameter of 42 in, which formula will she use? The circumference or distance around a circle is π times

Standard deviation, Certain model of new home distributed with a mean of $1...

Certain model of new home distributed with a mean of $150,000. Find percentage of buyers who paid between $150,000-155,000 if standard deviation is $1800.

Cartesian graph of density of water - temperature, Cartesian Graph of Densi...

Cartesian Graph of Density of Water - Temperature: Example:  The  density  of  water  was  measured  over  a  range  of  temperatures.   Plot the subsequent recorded data on

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