Question

1,Tìm nghiệm của các đa thức sau:

a, f(x)= \(x^{3}\)+2x-\(6x^{2}\)

b, N(x)= -2-x-x²

2, Cho f(x)=ax²+bx+c.

Xac dinh a; b; c biet f (x) co hai nghiem la 2 va -2; a la so lon hon c la 3 don vi

Answer 1

Câu 2: 

Theo đề, ta có:

\(\left\{{}\begin{matrix}a-c=3\\f\left(2\right)=0\\f\left(-2\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(c+3\right)\cdot2^2+b\cdot2+c=0\\\left(c+3\right)\cdot\left(-2\right)^2+b\cdot\left(-2\right)+c=0\\a=c+3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}4\left(c+3\right)+2b+c=0\\4\left(c+3\right)-2b+c=0\\a=c+3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5c+12+2b=0\\5c+12-2b=0\\a=c+3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}b=0\\c=-\dfrac{12}{5}\\a=c+3=-\dfrac{12}{5}+3=\dfrac{3}{5}\end{matrix}\right.\)