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

Solutions to systems, Now that we've found some of the fundamentals out of ...

Now that we've found some of the fundamentals out of the way for systems of differential equations it's time to start thinking about how to solve a system of differential equations

Pricing styrategies, #questiThe net profit in an appliance department for t...

#questiThe net profit in an appliance department for the spring /sumeer was $20,000 which represented 2% of net sales. Operating expenses total $480,000 find dollar amount of gross

Example of infinite interval - improper integrals, Evaluate the subsequent ...

Evaluate the subsequent integral. Solution This is an innocent enough looking integral. Though, because infinity is not a real number we cannot just integrate as norm

Quadratic equation, find a quadratic equation whose roots are q+1/2 and 2p-...

find a quadratic equation whose roots are q+1/2 and 2p-1 with p+q=1

Formula to know the area of fan will wrap, Aaron is installing a ceiling fa...

Aaron is installing a ceiling fan in his bedroom. Once the fan is in motion, he requires to know the area the fan will wrap. What formula will he use? The area of a circle is π

Hyperboloid of two sheets - three dimensional spaces, Hyperboloid of Two Sh...

Hyperboloid of Two Sheets The equation which is given here is the equation of a hyperboloid of two sheets. - x 2 /a 2 - y 2 / b 2 + z 2 /c 2 = 1 Here is a diagram of

Probability, A man is known to speak truth 3 out of 4 times.He throws adi...

A man is known to speak truth 3 out of 4 times.He throws adie and reports it is a six. Find the probability that it is actually a six. Solution)  we can get a six if a man s

Percentage profit and loss, #a grocer buys a box of 200oranges for $25 he s...

#a grocer buys a box of 200oranges for $25 he sells them for 15c caluclate his percentage profit

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