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}

Asked Apr 1, 2011 by Hayden (270 points) edited Jun 15, 2013 by Community

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!

Answered Apr 1, 2011 by Matt Sullivan (1,160 points) edited Jun 15, 2013 by Community

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

Answered## 1 Answer