Question

Write a quadratic function h whose only zero is 5

h(x)=

Answer 1

well, is a quadratic, so it has two roots, in this case that'll be 5 only per se, is really 5 but twice, or we should say it has a root of 5 with multiplicity of 2, that gives us

`\begin{cases} x = 5 &\implies x -5=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -5 )( x -5 ) = \stackrel{0}{h}}\hspace{5em}\stackrel{\textit{assuming}}{a=1}\hspace{5em}1(x-5)(x-5)=h(x) \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-10x+25=h(x) \end{array}}~\hfill`