## Question

# How many real number solutions are there to the equation 3x^{2} - x + 4 = 0

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

## Answer : The quadratic equation 3x^{2} - x + 4 = 0 has 0 real solutions .

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

**Explanation : **

For the quadratic equation 3x^{2} - x + 4 = 0 .

Let us calculate the discriminant that is b^{2} - 4ac (General form of the quadratic equation is ax^{2} + bx + c)

Hence, the discriminant for quadratic equation 3x^{2} - x + 4 = 0 is -47.

Since the discriminant of the quadratic equation 3x^{2} - x + 4 = 0 is negative, the given quadration has complex roots.

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

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