Write a polynomial equation of degree 4 that has the following roots: -1 repeated three times and 4.
\(\bf \begin{cases}
x=-1\to x+1=0\to &(x+1)=0\\
x=-1\to x+1=0\to &(x+1)=0\\
x=-1\to x+1=0\to &(x+1)=0\\
x=4\to x-4=0\to &(x-4)=0
\end{cases}
\\\\\\
(x+1)(x+1)(x+1)(x-4)=0\implies (x+1)^3(x-4)=0
\\\\\\
(x+1)^3(x-4)=\textit{original polynomial}\)
those are the roots, multiply them, to get the polynomial
Answer:
\(f(x)= (x+1)^3(x-4)\)
Step-by-step explanation:
a polynomial equation of degree 4 that has the following roots: -1 repeated three times and 4.
-1 is repeated three times
so roots are -1,-1, -1,4
We write the roots in factor form
If 'a' is a root then (x-a) is a factor
roots are -1,-1, -1,4
Factors are (x+1)(x+1)(x+1)(x-4)
\(f(x)= (x+1)(x+1)(x+1)(x-4)\)
\(f(x)= (x+1)^3(x-4)\)