Question

 use the discriminant to determine how many and what kind of solution to quadric equation X ^2- X = -1/4 

Answer 1

To determine the number and type of solutions to the quadratic equation x^2 - x = -1/4, we can use the discriminant, which is the part of the quadratic formula that determines the number of solutions. The quadratic formula is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. In this case, the coefficients of the equation are a = 1, b = -1, and c = -1/4. Plugging these values into the formula gives us:

x = (1 +/- sqrt(1^2 - 4(1)(-1/4))) / (2(1))

x = (1 +/- sqrt(1 + 1)) / 2

x = (1 +/- sqrt(2)) / 2

Therefore, the quadratic equation has two solutions: x = (1 + sqrt(2)) / 2 and x = (1 - sqrt(2)) / 2. These solutions are both real numbers.