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

User Akatran
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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
User Vasiliy
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