To find the discriminant of the quadratic equation \( 8t^2 + 8t + 2 = 0 \), we can use the formula for the discriminant \( D \) given by:
\[ D = b^2 - 4ac \]
where \( a \), \( b \), and \( c \) are the coefficients from the quadratic equation in the standard form \( at^2 + bt + c = 0 \).
In this equation:
- \( a = 8 \)
- \( b = 8 \)
- \( c = 2 \)
Now we can substitute these values into the discriminant formula:
\[ D = (8)^2 - 4(8)(2) \]
Calculating \( D \):
\[ D = 64 - 4 \cdot 8 \cdot 2 \] \[ D = 64 - 64 \] \[ D = 0 \]
So, the discriminant of the quadratic equation \( 8t^2 + 8t + 2 = 0 \) is \( 0 \). This indicates that the equation has one real double root.
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