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

How long will it take to dispense 330 gallons, A large pipe dispenses 750 g...

A large pipe dispenses 750 gallons of water in 50 seconds. At this rate, how long will it take to dispense 330 gallons? Find out the number of gallons per second by dividing 75

Mixing problems, In these problems we will begin with a substance which is ...

In these problems we will begin with a substance which is dissolved in a liquid. Liquid will be entering as well as leaving a holding tank. The liquid entering the tank may or may

Solve the radical form, Simplify following. Suppose that x, y, & z are posi...

Simplify following. Suppose that x, y, & z are positive.                      √ y 7 Solution In this case the exponent (7) is larger than the index (2) and thus the fir

Activity on Node, schedulling problem with variability in task times

schedulling problem with variability in task times

Pendulum, how many pendulum swings will it take to walk across the classroo...

how many pendulum swings will it take to walk across the classroom

Describe laws of cosines, Q. Describe Laws of Cosines? The law of cosin...

Q. Describe Laws of Cosines? The law of cosines is used to find the missing piece of a triangle if we are given either 1. Two sides and the included angle (SAS) or  2. All t

The blood pressure over two heart beats, At rest, the human heart beats onc...

At rest, the human heart beats once every second. At the strongest part of the beat, a person's blood pressure peaks at 120mmHg. At the most relaxed part of the beat, a person's bl

Definition and theorem of derivation, Definition : A function f ( x ) is c...

Definition : A function f ( x ) is called differentiable at x = a if f ′ ( x ) exists & f ( x ) is called differentiable onto an interval if the derivative present for each of the

Help, draw a right angle isosceles triangle with 9 triangles in it

draw a right angle isosceles triangle with 9 triangles in it

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