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

Product rule, Product Rule If the two functions f(x) & g(x) are differe...

Product Rule If the two functions f(x) & g(x) are differentiable (i.e. the derivative exist) then the product is differentiable and,

Circles, alternate segment theorum

alternate segment theorum

Determine the tangent line to f ( x ) = 15 - 2x2 at x = 1, Determine the t...

Determine the tangent line to f ( x ) = 15 - 2x 2   at x = 1. Solution : We know from algebra that to determine the equation of a line we require either two points onto the li

Consumer behaviour.., consumer behaviour in my feild of studies accounting ...

consumer behaviour in my feild of studies accounting ..

Bussiness, How do these websites help the company strengthen its relationsh...

How do these websites help the company strengthen its relationships with its stakeholders? List the website(s) that you previewed and give examples to support your answers. Who are

Convex rectilinear figure, the sum of the interior angles of a convex recti...

the sum of the interior angles of a convex rectilinear figure is equal to sum of the exterior angles. then the number of sides is

Four-step plan, Adison earned $25 mowing her neighbor''s lawn. Then she loa...

Adison earned $25 mowing her neighbor''s lawn. Then she loaned her friend $18, and got $50 from her grandmother for her birthday. She now has $86. How much money did Adison have to

Geometric interpretation of the cross product, Geometric Interpretation of ...

Geometric Interpretation of the Cross Product There is as well a geometric interpretation of the cross product.  Firstly we will let θ be the angle in between the two vectors a

Scatter graphs, Scatter Graphs - A scatter graph is a graph that compr...

Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin

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