+1

For what values of m will the following equation have equal roots?

\begin{equation}
(m+1)x^2+2(m+3)x+4m+5=0
\end{equation}


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1 Answer

+1

A quadratic has only one solution (equal roots) if the discriminant is 0

The discriminant = b^2-4ac where y=ax^2+bx+c

\begin{equation}
a=(m+1) b=2(m+3) c=4m+5
\end{equation}

So:

\begin{equation}
0=[2(m+3)]^2-4*(m+1)(4m+5)
\end{equation}

\begin{equation}
0=4(m^2+6x+9)-4(4m^2+9m+5)
\end{equation}

\begin{equation}
0=4m^2+24m+36-16m^2-36m-20
\end{equation}

\begin{equation}
0=-12m^2-12m+16
\end{equation}

\begin{equation}
0=3m^2+3m-4
\end{equation}

\begin{equation}
m=(sqrt(57)-3)/6 or m=-(sqrt(57)+3)/6
\end{equation}

In the second last step, I divided each step by -4

In the last step, I used the quadratic formula.

Feel free to ask any questions.

Hope that helps!


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