Answer: NO SOLUTIONS
Explanation:
The number of real solutions for a quadratic equation can be determined by its discriminant, which is the value inside the square root of the quadratic formula:
Discriminant (Δ) = b² - 4ac
In the equation you provided, 3x² - x + 5 = 0, the coefficients are as follows:
a = 3
b = -1
c = 5
Now, calculate the discriminant:
Δ = (-1)² - 4 * 3 * 5
Δ = 1 - 60
Δ = -59
The discriminant is negative (Δ < 0). When the discriminant is negative, the quadratic equation has no real solutions. Therefore, the equation 3x² - x + 5 = 0 has no real solutions.