Question

Find the values of a and b if x+1 and x-2 are factors of 3x^3-ax^2+bx+2

Answer 1

@mathmath333 @ganeshie8

Answer 2

if \(x+1\) and \(x-2\) are the factors of
\(\large\tt \begin{align} \color{black}{f(x)=3x^3-ax^2+bx+2}\end{align}\)
then
\(\large\tt \begin{align} \color{black}{f(-1) =f(2) =0}\end{align}\)

Answer 3

\(\large\tt \begin{align} \color{black}{f(x)=3x^3-ax^2+bx+2\\~\\
f(-1) =3(-1)^3-a(-1)^2+b(-1)+2=0\\~\\
a+b=-1----\color{red}{(1)}\\~\\
f(2) =3(2)^3-a(2)^2+b(2)+2=0\\~\\
2a-b=13-------\color{red}{(2)}\\~\\
}\end{align}\)