Show that the following three polynomials in <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="

Diya Moreno

Diya Moreno

Answered question

2022-06-03

Show that the following three polynomials in R [ x ]
x 2 / 2 x / 2 , 1 x 2 , x 2 / 2 + x / 2

Answer & Explanation

Adrianna Barnes

Adrianna Barnes

Beginner2022-06-04Added 3 answers

a P 1 ( x ) + b P 2 ( x ) + c P 3 ( x ) = 0
a ( x 2 2 x 2 ) + b ( 1 x 2 ) + c ( x 2 2 + x 2 ) = 0
( a 2 b + c 2 ) x 2 + ( a 2 + c 2 ) x + b = 0
By applying the Identity Theorem for polynomials, we get that
{ a 2 b + c 2 = 0 a 2 + c 2 = 0 b = 0
{ a 2 + c 2 = 0 a 2 + c 2 = 0 b = 0
{ a + c = 0 a + c = 0 b = 0
{ a + c = 0 c = a b = 0
{ 2 a = 0 c = a b = 0
{ a = 0 c = 0 b = 0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?