How Cheenta works to ensure student success?

Explore the Back-StoryThis is a Test of Mathematics Solution Subjective 175 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

** Let be a polynomial with integer coefficients,such that, are odd integers.Show that**

**(a) does not have any even integer roots. **

**(b) does not have any odd integer roots.**

Given the two statements **(a) and (b) ** above it is clear that if we can prove that has no integer roots,then we are done.

** **Let us assume has an integer root .

Then we can write,

where,is any function of .

Now ,putting in ,we get

and,

now as and ,are consecutive integers and

cannot be both odd,

which means that cannot be both odd,given whatever are.

So,it is a contradiction!!.

So,we can conclude that there exists no integer solution of .

Hence,we are done.

This is a Test of Mathematics Solution Subjective 175 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

** Let be a polynomial with integer coefficients,such that, are odd integers.Show that**

**(a) does not have any even integer roots. **

**(b) does not have any odd integer roots.**

Given the two statements **(a) and (b) ** above it is clear that if we can prove that has no integer roots,then we are done.

** **Let us assume has an integer root .

Then we can write,

where,is any function of .

Now ,putting in ,we get

and,

now as and ,are consecutive integers and

cannot be both odd,

which means that cannot be both odd,given whatever are.

So,it is a contradiction!!.

So,we can conclude that there exists no integer solution of .

Hence,we are done.

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIALAcademic Programs

Free Resources

Why Cheenta?