Question

cho đa thức sau : A(x)=x³+4x²-5x+2 ; B(x)=2x³+x²-5x-7; C(x)=x³+x²

^{a) tính M(x)=A(x)-B(x)+C(x)}

^{b) tìm nghiệm của M(x)}

Answer 1

Câu a :

\(M\left(x\right)=A\left(x\right)-B\left(x\right)+C\left(x\right)\)

\(=\left(x^3-4x^2-5x+2\right)-\left(2x^3+x^2-5x-7\right)+\left(x^3+x^2\right)\)

\(=x^3-4x^2-5x+2-2x^3-x^2+5x+7+x^3+x^2\)

\(-4x^2+9\)

Câu b :

\(M\left(x\right)=0\Leftrightarrow-4x^2+9=0\)

\(\Leftrightarrow-\left(2x-3\right)\left(2x+3\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\2x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)

Vậy \(x=-\dfrac{3}{2}\) hoặc \(x=\dfrac{3}{2}\)