Answer:
(x-4)x = 0
Explanation:
If we have a quadratic equation of the form
[tex](x-a)(x-b)=0[/tex]it has solutions at x = a and x = b because putting either one of these values into the above equation satisfies it. For example, putting in x = a gives
[tex]\begin{gathered} (a-a)(x-b)=0 \\ 0(x-b)=0 \\ 0=0 \end{gathered}[/tex]this satisfies the equation and likewise for x = b.
Hence, if we want to construct an equation which has solutions x = 4 and x = 0, we just need to set a = 4 and b = 0. Doing this gives
[tex]\begin{gathered} (x-4)(x-0)=0 \\ (x-4)x=0 \end{gathered}[/tex]which is a polynomial that has the solutions desired.
