To find the discriminant of the quadratic equation \( 8t^2 + 8t + 2 = 0 \), we use the formula for the discriminant given by:
\[ D = b^2 - 4ac \]
In this case, the coefficients \( a \), \( b \), and \( c \) are as follows:
- \( a = 8 \)
- \( b = 8 \)
- \( c = 2 \)
Now, we substitute these values into the formula:
\[ D = 8^2 - 4 \cdot 8 \cdot 2 \] \[ D = 64 - 64 \] \[ D = 0 \]
The discriminant of the quadratic equation \( 8t^2 + 8t + 2 = 0 \) is \( D = 0 \). This means that the equation has one real double root.
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