Question

Write a polynomial of least degree with roots 1 and 4

Answer 1

`\begin{cases} x = 1 &\implies x -1=0\\ x = 4 &\implies x -4=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -1 )( x -4 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{assuming a = 1}}{1( x -1 )( x -4 ) = y}\implies \boxed{x^2-5x+4=y}`