Question

Write the quadratic equation whose roots are -2 and 3, and whose leading coefficient is 3

Answer 1

now, if the roots are -2 and 3, that simply means
`\bf \begin{cases} x=-2\implies &x+2=0\\ x=3\implies &x-3=0 \end{cases}`

now, as far as the leading term's coefficient having a 3, we can simply make it a "common factor" of both terms.


`\bf \begin{cases} x=-2\implies &x+2=0\\ x=3\implies &x-3=0 \end{cases}\implies (x+2)(x-3)=0 \\\\\\ \stackrel{\textit{common factor}}{3}(x+2)(x-3)=\textit{original polynomial} \\\\\\ 3(x^2-x-6)=y\implies 3x^2-3x-18=y`