How many real number solutions does the equation have? 0 = - 4x^2 + 7x -8
a. no solution*****
b. one solution
c. two solutions
d. infinitely many solutions
X = (-B +-sqrt(B^2-4AC)/2A.
X = (-7 +-sqrt(49-128))/-8.
The quantity under radical is negative: No solutions.
To determine the number of real number solutions that the equation 0 = -4x^2 + 7x - 8 has, we can use the discriminant of the quadratic equation.
The discriminant (represented as Δ) is calculated using the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, the equation is -4x^2 + 7x - 8 = 0, so the coefficients are:
a = -4
b = 7
c = -8
Substituting these values into the discriminant formula, we have:
Δ = (7)^2 - 4(-4)(-8)
Δ = 49 - 128
Δ = -79
Since the discriminant is negative (Δ < 0), it means the quadratic equation has no real number solutions. Therefore, the correct answer is option a) no solution.