Question

Answer 1

a.

\(P\left(x\right)=x^4+2x^3-5x+\dfrac{1}{2}\)

\(Q\left(x\right)=x^4+2x^3-4x^2-5x+\dfrac{3}{2}\)

b.

\(M\left(x\right)=x^4+2x^3-5x+\dfrac{1}{2}-\left(x^4+2x^3-4x^2-5x+\dfrac{3}{2}\right)\)

\(M\left(x\right)=4x^2-1\)

\(M\left(x\right)=0\Rightarrow4x^2-1=0\)

\(\Leftrightarrow\left(2x-1\right)\left(2x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)