Consider the quadratic equation. \( -t^{2}-9 t-7=0 \) State the values of \( a, b, c \), in the standard form of a quadratic equation. \( a=\square \) \( b=\square \) Determine the value of the discriminant, \( D=\square \) Since the discriminant is Select an answer \( \vee \), there will be Hint: Enter the number of real solutions.

To analyze the quadratic equation \( -t^{2}-9t-7=0 \), we first need to express it in the standard form of a quadratic equation, which is given by: \[ at^2 + bt + c = 0 \] From the equation \( -t^{2}-9t-7=0 \), we can identify the coefficients: 1. \( a = -1 \) 2. \( b = -9 \) 3. \( c = -7 \) Now, we can summarize the values: \[ a = -1 \] \[ b = -9 \] \[ c = -7 \] Next, we will calculate the discriminant \( D \) using the formula: \[ D = b^2 - 4ac \] Substituting the values of \( a \), \( b \), and \( c \): \[ D = (-9)^2 - 4(-1)(-7) \] Now, let's calculate \( D \): \[ D = 81 - 28 \] \[ D = 53 \] Now we have: \[ D = 53 \] Since the discriminant \( D \) is greater than zero (\( D > 0 \)), this indicates that there will be two distinct real solutions. To summarize: - The values are: - \( a = -1 \) - \( b = -9 \) - \( c = -7 \) - The value of the discriminant is: - \( D = 53 \) - Since the discriminant is greater than zero, there will be **two distinct real solutions**.