Question

Determine the number of real solutions:
1. y=-3x^2+x+12

Answer 1

2

Explanation:

To determine the number of real solutions of the quadratic equation `y = -3x^2 + x + 12`, we can use the discriminant formula `b^2 - 4ac`.

First, we identify the values of a, b, and c:

a = -3

b = 1

c = 12

Next, we substitute these values into the discriminant formula:

b^2 - 4ac = (1)^2 - 4(-3)(12) = 145

Since the discriminant is positive (and not equal to zero), the quadratic equation has two distinct real roots. Therefore, the number of real solutions is 2.