Given:
We will write the equation for the quadratic equation that will have solutions of x = 12 and x = 2
So, the factors of the equation will be:
(x - 12), and (x-2)
So, the factored form of the equation will be:
[tex](x-12)(x-2)=0[/tex]Expand the equation to write it in standard form:
[tex]\begin{gathered} (x-12)(x-2)=0 \\ x(x-2)-12(x-2)=0 \\ x^2-2x-12x+24=0 \\ x^2-14x+24=0 \end{gathered}[/tex]So, the answer will be, the quadratic equation is:
[tex]x^{2}-14x+24=0[/tex]