How many real-number solutions does the equation have? 0 equals 3 x squared minus 5x minus 5

1 answer

The given equation is 0 = 3x^2 - 5x - 5.

To determine the number of real-number solutions the equation has, we need to use the discriminant of the quadratic equation.

The discriminant is given by b^2 - 4ac, where a, b, and c are the coefficients of x^2, x, and the constant term in the quadratic equation, respectively.

In this case, a = 3, b = -5, and c = -5.

Therefore, the discriminant is (-5)^2 - 4*3*(-5) = 25 + 60 = 85.

Since the discriminant is positive (85 > 0), the quadratic equation has two distinct real-number solutions. So, the given equation has 2 real-number solutions.