Show that p ( x ) = 2 x3 - 5x2 -10 x + 5 intermediate value , Mathematics

Assignment Help:

Example   Show that p ( x ) = 2 x3 - 5x2 -10 x + 5 has a root somewhere in the interval [-1,2].

Solution What we're actually asking here is whether or not the function will take on the value

                                                        p ( x ) = 0

somewhere among -1 and 2.  In other terms, we desire to show that there is a number c such that -1 < c < 2 and p (c ) = 0 .  Though if we described M = 0 and acknowledge that a = -1 and b = 2 we can distinguish that these two condition on c are precisely the conclusions of the Intermediate Value Theorem.

Thus, this problem is set up to employ the Intermediate Value Theorem and actually, all we need to do is to illustrates that the function is continuous and that M = 0 is among p ( -1) and p ( 2) (that means p ( -1) < 0 < p ( 2) or p (2) < 0 < p (-1) and we'll be done.

To do this all we have to do is compute,

p ( -1) = 8                   p ( 2) = -19

Hence, we have,

-19 = p ( 2) < 0 < p ( -1) = 8

Therefore M = 0 is among p ( -1) and p ( 2) and as p ( x ) is a polynomial it's continuous everywhere and thus particularly it's continuous on the interval [-1,2].  Thus by the Intermediate Value Theorem there has to be a number -1 < c < 2 so that,

                                                    p (c ) = 0

Thus the polynomial does have a root among -1 & 2.

For the sake of completeness here is a graph illustrating the root that just we proved existed. Note as well that we utilized a computer program to in fact find the root and that the Intermediate Value

Theorem did not tell us what this value was.

2328_Theorem.png


Related Discussions:- Show that p ( x ) = 2 x3 - 5x2 -10 x + 5 intermediate value

Quantitative Techniques, The following table given the these scores and sal...

The following table given the these scores and sales be nine salesman during last one year in a certain firm: text scores sales (in 000''rupees) 14 31 19

Shares and dividends, at what price 6.25% rs 100 share be quoted when the m...

at what price 6.25% rs 100 share be quoted when the money is worth 5%

Correlation, How o make vicariate frequency distribution table

How o make vicariate frequency distribution table

Draw the direction field, Draw the direction field for the subsequent diffe...

Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation.   Solution:  y′ = y - x  To draw direct

Most crucial aspect of learning multiplication, Which of the following is t...

Which of the following is the most crucial aspect of learning multiplication? i) Multiplication facts ii) Recall of tables and their recitation iii) Understanding "how man

Geometry help, A painter leans a 10-foot ladder against the house she is to...

A painter leans a 10-foot ladder against the house she is to paint. The foot of the ladder is 3 feet from the house. How far above the ground does the ladder touch the house? Appro

What is perfect squares, What is Perfect Squares ? Any number that can ...

What is Perfect Squares ? Any number that can be written as an integer to the power of two is called a perfect square. For example, 4 can be written as 2 2 4 is a "perfect sq

Constants of integration, CONSTANTS OF INTEGRATION Under this section w...

CONSTANTS OF INTEGRATION Under this section we require to address a couple of sections about the constant of integration. During most calculus class we play pretty quick and lo

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

Solution to an initial value problem, S olve the subsequent IVP. dv/dt =...

S olve the subsequent IVP. dv/dt = 9.8 - 0.196v;               v(0) = 48 Solution To determine the solution to an Initial Value Problem we should first determine the gen

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