Final answer:
The discriminant of the quadratic equation −45d^2+4d−1=0 is calculated using the formula b² - 4ac, resulting in a negative value of −164, indicating that the quadratic equation has no real number solutions.
Step-by-step explanation:
To find the discriminant of the quadratic equation −45d^2+4d−1=0, we will use the formula b² - 4ac, where a, b, and c are the coefficients from the quadratic equation at² + bt + c = 0. In this case, a = −45, b = 4, and c = −1.
Substituting these values into the discriminant formula gives us:
Discriminant = 4² - 4(−45)(−1) = 16 - 4(-45)(-1) = 16 - 180 = −164.
Since the discriminant is negative (−164), it means the quadratic equation has no real number solutions but rather two complex solutions. Therefore, the correct answer is b) Negative.