Question

Find the discriminant.
8t2+8t+2=0

Answer 1

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.