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Akimi4 [234]
3 years ago
10

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

Mathematics
1 answer:
KIM [24]3 years ago
5 0
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
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