# Question #4195c

Sep 17, 2017

$m = - 2$

#### Explanation:

When a quadratic equation has twin roots, its discriminant $\Delta$ is equal to zero.

The formula for the discriminant is $\Delta = {b}^{2} - 4 a c$.

Let's evaluate the discriminant of our quadratic equation:

$R i g h t a r r o w \Delta = {\left(8 - 2 m\right)}^{2} - 4 \left(1 - m\right) \left(12\right)$

$R i g h t a r r o w \Delta = 64 - 32 m + 4 {m}^{2} - 12 \left(4 - 4 m\right)$

$R i g h t a r r o w \Delta = 64 - 32 m + 4 {m}^{2} - 48 + 48 m$

$R i g h t a r r o w \Delta = 4 {m}^{2} + 16 m + 16$

Then, let's set it equal to zero:

$R i g h t a r r o w \Delta = 0$

$R i g h t a r r o w 4 {m}^{2} + 16 m + 16 = 0$

$R i g h t a r r o w 4 \left({m}^{2} + 4 m + 4\right) = 0$

$R i g h t a r r o w {m}^{2} + 4 m + 4 = 0$

Now, let's factorise the equation using the middle-term break:

$R i g h t a r r o w {m}^{2} + 2 m + 2 m + 4 = 0$

$R i g h t a r r o w m \left(m + 2\right) + 2 \left(m + 2\right) = 0$

$R i g h t a r r o w \left(m + 2\right) \left(m + 2\right) = 0$

$R i g h t a r r o w {\left(m + 2\right)}^{2} = 0$

$R i g h t a r r o w m + 2 = 0$

$\therefore m = - 2$