Question
How many real-number solutions does the equation have?
0=3x^2-5x-5
1 one solution
2 two solutions
3 no solutions
4 infinitely many solutions
To determine the number of real-number solutions of the equation, you can use the discriminant of the quadratic equation in standard form, ax^2 + bx + c = 0. The discriminant is the expression b^2 - 4ac.
In this case, the equation is 0 = 3x^2 - 5x - 5, so a = 3, b = -5, and c = -5. The discriminant is then calculated as follows:
b^2 - 4ac = (-5)^2 - 4(3)(-5) = 25 + 60 = 85
Since the discriminant of the equation is positive (85 > 0), the equation has 2 real-number solutions.