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

Determine the length of the longer base, The longer base of a trapezoid is ...

The longer base of a trapezoid is 3 times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the trape

Undetermined coefficients, In this section we will see the first method whi...

In this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equation. y′′ + p (t ) y′ + q (t ) y = g (t) One of

Do all our activities involve mathematics?, Do All Our Activities Involve M...

Do All Our Activities Involve Mathematics? :  The answer to this is 'yes' and 'no'. For those who look for mathematics and know where to look for it, it is 'yes'. For those who do

Example of word problems involving money, Example of Word Problems Involvin...

Example of Word Problems Involving Money: A collection of coins consists of nickels, dimes & quarters. The number of quarters is double the number of nickels, and the number o

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

draw a right angle isosceles triangle with 9 triangles in it

Proof of various integral facts- formulas, PROOF OF VARIOUS INTEGRAL FACTS/...

PROOF OF VARIOUS INTEGRAL FACTS/FORMULAS/PROPERTIES In this section we've found the proof of several of the properties we saw in the Integrals section and also a couple from t

How to convert decimals to fractions, Q. How to Convert decimals to fractio...

Q. How to Convert decimals to fractions? Ans. Note: This tutorial covers only terminating decimals.

Find out the roots of the quadratic equation, Find out the roots of the fol...

Find out the roots of the following quadratic equation. 3x 2 + 7x = 0 Solution: Using Equation 6, one root is determined. x = 0 Using Equation 7, substitute the

Simplify, X^2 – y^2 – 2y - 1

X^2 – y^2 – 2y - 1

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