To find the discriminant of the equation -1 = 5x^2 - 2x, we need to consider the quadratic equation in the form of ax^2 + bx + c = 0, where a = 5, b = -2, and c = -1.
The discriminant (D) is calculated using the formula D = b^2 - 4ac. Substituting the values into the formula:
D = (-2)^2 - 4(5)(-1)
= 4 + 20
= 24
The discriminant has a value of 24.
The value of the discriminant determines the nature and number of real solutions of a quadratic equation. Here's what different values of the discriminant indicate:
1. If the discriminant (D) is positive (D > 0), it means there are two distinct real solutions for the quadratic equation.
2. If the discriminant is zero (D = 0), it means there is one real solution (a double root) for the quadratic equation.
3. If the discriminant is negative (D < 0), it means there are no real solutions, and the equation has complex roots.
In this case, since the discriminant has a positive value of 24, it indicates that the equation -1 = 5x^2 - 2x has two distinct real solutions.