Question

how many real number Solutions does the equation have negative 8 x ^ 2 - 8 x - 2 equals 0

Answer 1

The equation has one real number solution

Here, we want to get the numeber of real number solutions the equation has

We proceed as follows;

$\begin{gathered} -8x^2-8x-2\text{ = 0} \\ -8x^2-4x-4x-2\text{ = 0} \\ -4x(2x+1)-2(2x+1)\text{ =0} \\ (2x+1)(-4x-2)=\text{ 0} \\ 2x\text{ + 1 = 0 or -4x-2 = 0} \\ 2x\text{ = -1 or -4x = 2} \\ x\text{ = -1/2 or x = 2/-4} \\ x\text{ = -1/2 twice} \end{gathered}$

The equation has a repeating root

Thus, we can say that the equation has only one real number solution