How many real number solutions are there to the equation 3x² - x + 4 = 0

We will use the concept of a quadratic equation to find the numbers of real number solutions of the equation.

Answer: The quadratic equation 3x² - x + 4 = 0 has 0 real solutions

Let us see how we will use the concept of a quadratic equation to find the numbers of real number solutions of the equation.

Explanation : 

For the quadratic equation 3x² - x + 4 = 0 .

Let us calculate the discriminant that is b² - 4ac  (General form of the quadratic equation is ax² + bx + c)

Hence, the discriminant for quadratic equation 3x² - x + 4 = 0 is -47.

Since the discriminant of the quadratic equation 3x² - x + 4 = 0  is negative, the given quadration has complex roots.

Hence, the quadratic equation has imaginary roots and no real solutions.