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

Indices, 4n to the power 3/2 = 8 to the power minus 1/3. find the value of ...

4n to the power 3/2 = 8 to the power minus 1/3. find the value of n.

Finding the inverse of a function , Finding the Inverse of a Function : Th...

Finding the Inverse of a Function : The procedure for finding the inverse of a function is a rather simple one although there are a couple of steps which can on occasion be somewh

Calculate the area of rectangle , Calculate the area of RECTANGLE ? Th...

Calculate the area of RECTANGLE ? The area of a rectangle is the amount of space taken up by a rectangle, which is a two-dimensional shape. You find the area (A) of a recta

Math, The Timbuktu post office has only 3 cents and 7 cents stamps having r...

The Timbuktu post office has only 3 cents and 7 cents stamps having run out of all other denominations. What are the six amounts of postage that cannot be created? How do you know

Parabola, please i need the answers to x^_7x+10 i want the vertex,axis of s...

please i need the answers to x^_7x+10 i want the vertex,axis of semetery,y intersect and the x intercept

Define period, Q. Define Period, Amplitude and Phase Shift? Ans. P...

Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest

Absolute mean deviation-measures of central tendency, Illustration 1 I...

Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60

Algebra, (x+15)/y=10 where y=5

(x+15)/y=10 where y=5

Gravity, There is a list of the forces which will act on the object. Gr...

There is a list of the forces which will act on the object. Gravity, F g The force because of gravity will always act on the object of course. Such force is F g   = mg

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